To solve this equation, we need to combine like terms on both sides and then simplify:

2x^2 - 2x + 34 = -6x^2 - 34x + 10

First, let's bring all the terms to one side of the equation:

2x^2 - 2x + 34 + 6x^2 + 34x - 10 = 0

Combine the x^2 terms:

8x^2 - 2x + 34x - 10 = 0

Combine the x terms:

8x^2 + 32x - 10 = 0

Now, let's factor out the common factor:

2(4x^2 + 16x - 5) = 0

Now, we need to solve for x by setting each factor equal to zero:

4x^2 + 16x - 5 = 0

Using the quadratic formula, we find:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-16 ± √(16^2 - 44(-5))) / 2*4

x = (-16 ± √(256 + 80)) / 8

x = (-16 ± √336) / 8

x = (-16 ± 18.33) / 8

x = 2.33 or x = -3.33

So, the solutions to the equation are x = 2.33 or x = -3.33.