5x(2x-8)=32

Solution for 5x(2x-8)=32 equation:

5x(2x-8)=32

We move all terms to the left:

5x(2x-8)-(32)=0

We multiply parentheses

10x^2-40x-32=0

a = 10; b = -40; c = -32;
Δ = b2-4ac
Δ = -402-4·10·(-32)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-24\sqrt{5}}{2*10}=\frac{40-24\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+24\sqrt{5}}{2*10}=\frac{40+24\sqrt{5}}{20}
$