5x(2x-8)=90

Solution for 5x(2x-8)=90 equation:

5x(2x-8)=90

We move all terms to the left:

5x(2x-8)-(90)=0

We multiply parentheses

10x^2-40x-90=0

a = 10; b = -40; c = -90;
Δ = b2-4ac
Δ = -402-4·10·(-90)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{13}}{2*10}=\frac{40-20\sqrt{13}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{13}}{2*10}=\frac{40+20\sqrt{13}}{20}
$