Solve 6x^2+3x-18=0 Using The Quadratic Formula?

7 Answers

Oddman Profile
Oddman answered
The quadratic formula tells you the solution to
  ax^2 + bx + c = 0
is given by
  x = (-b ± √(b^2 - 4ac))/(2a)

You have an equation in which a=6, b=3, c=-18, so the formula gives
  x = (-3 ± √(3^2 - 4(6)(-18))/(2*6)
  x = (-3 ± √(9+432))/12
  x = (-3 ± √441)/12
  x = (-3 ± 21)/12
  x = {-24/12, 18/12}
  x = {-2, 3/2}
Aisha Profile
Aisha answered
This is simple:
 
6x2 + 3x - 18 = 0
Dividing the equation by 3, we get:
2x2 + x - 6 = 0
2x2 + 4x - 3x - 6 = 0
2x(x + 2) -3(x + 2)
(2x-3)(x+2)=0
x= 3/2
x=-2
Katie Harry Profile
Katie Harry answered
Shelia, first let's see what the quadratic formula is, ok?

x = [-b ±b2-4ac]/2a

Now, write out your equation:
6x2 + 3x -18 = 0

The values from the quadratic formula that we extract from this equation are:

a = 6
b = 3
c = -18

Now, all you have to do is put these values in the quadratic formula and you will get your answer
x = [-b ±b2-4ac]/2a

x =  [-3 ±32-4.6.-18]/2.6
(I am using a period to show a multiplication sign so that you do not confuse it with 'x' in the equation)

x = [-3 ± √9 + 432]/12
x = [-3
± √441]/12
x = [-3
± 21]/12

Now, the '
±' sign shows that the value can be either positive or negative.

So, we will solve for each. Now our two new equations are:

x = [-3 + 21]/12
x = 1.5

and

x = [-3 - 21]/12
x = -2

So, the two values for x are 1.5 and -2.

About how we type all the mathematical symbols, I use MS-Word for that. You can also use MS-Excel if you want to. Go to 'Insert' and choose 'Symbols'. Here, you would only be given a few options but an option would say, 'More symbols'. Choose that and you would probably find the symbol you are looking for.
I use MS-Office 2007. This also has inbuilt equations that you can choose from Insert 'Equations'. I think previous issues of Word would also have them. You just need to browse around a little. Use 'x' or '*' to show multiplication. You can square a number/ alphabet by writing it, like x2. Then select 2 and click on x2 on the tool bar to make it a superscript.
I think it would all be very clear to you now. Have fun!

John Nawrocki Profile
John Nawrocki answered
Since the question mentions the quadratic formula, the problem should probably read 6x2 + 3x – 18 = 0. The quadratic formula is shown in the picture. Following the formula, X= (-3+(SQRT(9-4*6*(-18))))/12 and x = (-3-(SQRT(9-4*6*(-18))))/12. Or, doing the arithmetic, x=1.5 and x=-2.
Aisha Profile
Aisha answered
Here is the solution:
6x2 + 3x - 18 = 0
6x2 +12x - 9x - 18= 0
6x(x+2) -9(x+2) = 0
(6x -9)(x+2)= 0
x = -2 is one answer
x= 9/6 or 2/3 is second answer
thanked the writer.
Anonymous
Anonymous commented
why didn't you divide the original equation by 3 at first? that's why you're second solution is wrong.
Emraan Varshani Profile
Emraan Varshani answered
Here is your quadratic equation :  6x2 + 3x – 18 = 0  therefore 6x(square)+12x-9x-18=0  6x(x+2)-9(x+2)=0  (6x-9)(x+2) = 0  therefore 6x-9 =0  and  x+2=0  therefore x=9/6 and x=-2    so the correct answer is x = {3/2, -2}      rough work    18 * 6 = 108  now can we take 12 * 9  like +12 and -9, which will sum up and  give +3{between} and the product 108{ product of first and the last 18 * 6 }
Fahad Hussain Profile
Fahad Hussain answered
If you need the answer then it will be (X=3/4, -2).

From equation a=6, b=3 and c=-18 and then put these values in quadratic formula, and then simplify this equation.

I hope you will get the answer very easily.

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