(2x-8)-(8x^2-6x+18)=(6x)-(64-6x+18)

Solution for (2x-8)-(8x^2-6x+18)=(6x)-(64-6x+18) equation:

(2x-8)-(8x^2-6x+18)=(6x)-(64-6x+18)

We move all terms to the left:

(2x-8)-(8x^2-6x+18)-((6x)-(64-6x+18))=0

We add all the numbers together, and all the variables

(2x-8)-(8x^2-6x+18)-(6x-(-6x+82))=0

We get rid of parentheses

-8x^2+2x+6x-(6x-(-6x+82))-8-18=0


We calculate terms in parentheses: -(6x-(-6x+82)), so:

6x-(-6x+82)

We get rid of parentheses

6x+6x-82

We add all the numbers together, and all the variables

12x-82

Back to the equation:

-(12x-82)


We add all the numbers together, and all the variables

-8x^2+8x-(12x-82)-26=0

We get rid of parentheses

-8x^2+8x-12x+82-26=0

We add all the numbers together, and all the variables

-8x^2-4x+56=0

a = -8; b = -4; c = +56;
Δ = b2-4ac
Δ = -42-4·(-8)·56
Δ = 1808
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:

$\sqrt{\Delta}=\sqrt{1808}=\sqrt{16*113}=\sqrt{16}*\sqrt{113}=4\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{113}}{2*-8}=\frac{4-4\sqrt{113}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{113}}{2*-8}=\frac{4+4\sqrt{113}}{-16}
$