Use the quadratic formula to solve. Express your answer in simplest form.6, x, squared, minus, 5, x, minus, 2, equals, minus, 6, x, squared6x 2 −5x−2=−6x 2

The given equation is 6x^2 - 5x - 2 = -6x^2.

First, we need to simplify the equation by moving all terms to one side.

This gives us 6x^2 + 6x^2 - 5x - 2 = 0.

Simplify further to get 12x^2 - 5x - 2 = 0.

Now, we can use the quadratic formula to solve for x. The quadratic formula is x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c.

In this case, a = 12, b = -5, and c = -2.

Substitute these values into the quadratic formula to get:

x = [5 ± sqrt((-5)^2 - 412(-2))] / (2*12) x = [5 ± sqrt(25 + 96)] / 24 x = [5 ± sqrt(121)] / 24 x = [5 ± 11] / 24

So the solutions are x = 16/24 = 2/3 and x = -6/24 = -1/4.