(-6x^2-x+8)=(6x^2+3x-2)

Solution for (-6x^2-x+8)=(6x^2+3x-2) equation:

(-6x^2-x+8)=(6x^2+3x-2)

We move all terms to the left:

(-6x^2-x+8)-((6x^2+3x-2))=0

We get rid of parentheses

-6x^2-x-((6x^2+3x-2))+8=0


We calculate terms in parentheses: -((6x^2+3x-2)), so:

(6x^2+3x-2)

We get rid of parentheses

6x^2+3x-2

Back to the equation:

-(6x^2+3x-2)


We add all the numbers together, and all the variables

-6x^2-1x-(6x^2+3x-2)+8=0

We get rid of parentheses

-6x^2-6x^2-1x-3x+2+8=0

We add all the numbers together, and all the variables

-12x^2-4x+10=0

a = -12; b = -4; c = +10;
Δ = b2-4ac
Δ = -42-4·(-12)·10
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{31}}{2*-12}=\frac{4-4\sqrt{31}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{31}}{2*-12}=\frac{4+4\sqrt{31}}{-24}
$