0=4x^2-12x-32

Solution for 0=4x^2-12x-32 equation:

0=4x^2-12x-32

We move all terms to the left:

0-(4x^2-12x-32)=0

We add all the numbers together, and all the variables

-(4x^2-12x-32)=0

We get rid of parentheses

-4x^2+12x+32=0

a = -4; b = 12; c = +32;
Δ = b2-4ac
Δ = 122-4·(-4)·32
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{41}}{2*-4}=\frac{-12-4\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{41}}{2*-4}=\frac{-12+4\sqrt{41}}{-8}
$