0=4x2-2x-32

Solution for 0=4x2-2x-32 equation:

0=4x^2-2x-32

We move all terms to the left:

0-(4x^2-2x-32)=0

We add all the numbers together, and all the variables

-(4x^2-2x-32)=0

We get rid of parentheses

-4x^2+2x+32=0

a = -4; b = 2; c = +32;
Δ = b2-4ac
Δ = 22-4·(-4)·32
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{129}}{2*-4}=\frac{-2-2\sqrt{129}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{129}}{2*-4}=\frac{-2+2\sqrt{129}}{-8}
$