There are several ways to interpret your question. Using the standard order of operations, it should be interpreted like this.

5/x = (10/3)*x + 4

5 = (10/3)x

(10/3)x

x

x = (-1.2 ±√(1.2

x = (-1.2 ±√(1.44+6))/2

x = -.6 ±√1.86

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A common error is to omit parentheses around the denominator expression. Assuming that error was made here, another way to interpret your question is

5/x = 10/(3x+4)

5(3x+4) = 10x (multiply both sides by x(3x+4))

15x + 20 = 10x (multiply it out)

5x + 20 = 0 (subtract 10x from both sides)

x + 4 = 0 (divide both sides by 5)

x = -4 (subtract 4 from both sides)

5/x = (10/3)*x + 4

5 = (10/3)x

^{2}+ 4x (multiply both sides by x)(10/3)x

^{2}+ 4x - 5 = 0 (subtract 5 from both sides; swap sides)x

^{2}+ 1.2 x - 1.5 = 0 (multiply both sides by 3/10)x = (-1.2 ±√(1.2

^{2}- 4(1)(-1.5)))/(2*1) (use the quadratic formula)x = (-1.2 ±√(1.44+6))/2

x = -.6 ±√1.86

_____

A common error is to omit parentheses around the denominator expression. Assuming that error was made here, another way to interpret your question is

5/x = 10/(3x+4)

5(3x+4) = 10x (multiply both sides by x(3x+4))

15x + 20 = 10x (multiply it out)

5x + 20 = 0 (subtract 10x from both sides)

x + 4 = 0 (divide both sides by 5)

x = -4 (subtract 4 from both sides)