5x(x+96)=90

Solution for 5x(x+96)=90 equation:

5x(x+96)=90

We move all terms to the left:

5x(x+96)-(90)=0

We multiply parentheses

5x^2+480x-90=0

a = 5; b = 480; c = -90;
Δ = b2-4ac
Δ = 4802-4·5·(-90)
Δ = 232200
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:

$\sqrt{\Delta}=\sqrt{232200}=\sqrt{900*258}=\sqrt{900}*\sqrt{258}=30\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-30\sqrt{258}}{2*5}=\frac{-480-30\sqrt{258}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+30\sqrt{258}}{2*5}=\frac{-480+30\sqrt{258}}{10}
$