The result will be
0 = 0
For the solution x = 1/3 (-2 - √10), you can get there like this.
3(1/3 (-2 - √10))^2 + 4(1/3 (-2 - √10)) - 2 = 0
3(1/9)(4 + 4√10 + 10) - 4/3(2 + √10) - 2 = 0
4/3 + (4/3)√10 + 10/3 - 8/3 - (4/3)√10 - 2 = 0 (multiply everything out, recognize 3/9 = 1/3)
(1/3)(4 + 10 - 8) - 2 + (√10)(4/3 - 4/3) = 0 (collect terms)
6/3 - 2 + 0*√10 = 0 (an intermediate step for the non-believers)
0 = 0
The same will obtain for the other solution with the exception that the signs on the √10 terms are reversed from - to + and vice versa.
0 = 0
For the solution x = 1/3 (-2 - √10), you can get there like this.
3(1/3 (-2 - √10))^2 + 4(1/3 (-2 - √10)) - 2 = 0
3(1/9)(4 + 4√10 + 10) - 4/3(2 + √10) - 2 = 0
4/3 + (4/3)√10 + 10/3 - 8/3 - (4/3)√10 - 2 = 0 (multiply everything out, recognize 3/9 = 1/3)
(1/3)(4 + 10 - 8) - 2 + (√10)(4/3 - 4/3) = 0 (collect terms)
6/3 - 2 + 0*√10 = 0 (an intermediate step for the non-believers)
0 = 0
The same will obtain for the other solution with the exception that the signs on the √10 terms are reversed from - to + and vice versa.
