-2(-x+4)4x-3=31

Solution for -2(-x+4)4x-3=31 equation:

-2(-x+4)4x-3=31

We move all terms to the left:

-2(-x+4)4x-3-(31)=0

We add all the numbers together, and all the variables

-2(-1x+4)4x-3-31=0

We add all the numbers together, and all the variables

-2(-1x+4)4x-34=0

We multiply parentheses

8x^2-32x-34=0

a = 8; b = -32; c = -34;
Δ = b2-4ac
Δ = -322-4·8·(-34)
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{33}}{2*8}=\frac{32-8\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{33}}{2*8}=\frac{32+8\sqrt{33}}{16}
$