(-7x-5)-(-3-8x);x=6

Solution for (-7x-5)-(-3-8x);x=6 equation:

(-7x-5)-(-3-8x)x=6

We move all terms to the left:

(-7x-5)-(-3-8x)x-(6)=0

We add all the numbers together, and all the variables

(-7x-5)-(-8x-3)x-6=0

We multiply parentheses

8x^2+(-7x-5)+3x-6=0

We get rid of parentheses

8x^2-7x+3x-5-6=0

We add all the numbers together, and all the variables

8x^2-4x-11=0

a = 8; b = -4; c = -11;
Δ = b2-4ac
Δ = -42-4·8·(-11)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{23}}{2*8}=\frac{4-4\sqrt{23}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{23}}{2*8}=\frac{4+4\sqrt{23}}{16}
$