5x(2x+20)=90

Solution for 5x(2x+20)=90 equation:

5x(2x+20)=90

We move all terms to the left:

5x(2x+20)-(90)=0

We multiply parentheses

10x^2+100x-90=0

a = 10; b = 100; c = -90;
Δ = b2-4ac
Δ = 1002-4·10·(-90)
Δ = 13600
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:

$\sqrt{\Delta}=\sqrt{13600}=\sqrt{400*34}=\sqrt{400}*\sqrt{34}=20\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{34}}{2*10}=\frac{-100-20\sqrt{34}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{34}}{2*10}=\frac{-100+20\sqrt{34}}{20}
$