0=5x^2-4x-32

Solution for 0=5x^2-4x-32 equation:

0=5x^2-4x-32

We move all terms to the left:

0-(5x^2-4x-32)=0

We add all the numbers together, and all the variables

-(5x^2-4x-32)=0

We get rid of parentheses

-5x^2+4x+32=0

a = -5; b = 4; c = +32;
Δ = b2-4ac
Δ = 42-4·(-5)·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{-(4)-4\sqrt{41}}{2*-5}=\frac{-4-4\sqrt{41}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{41}}{2*-5}=\frac{-4+4\sqrt{41}}{-10}
$