5x(180-x)=90

Solution for 5x(180-x)=90 equation:

5x(180-x)=90

We move all terms to the left:

5x(180-x)-(90)=0

We add all the numbers together, and all the variables

5x(-1x+180)-90=0

We multiply parentheses

-5x^2+900x-90=0

a = -5; b = 900; c = -90;
Δ = b2-4ac
Δ = 9002-4·(-5)·(-90)
Δ = 808200
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:

$\sqrt{\Delta}=\sqrt{808200}=\sqrt{900*898}=\sqrt{900}*\sqrt{898}=30\sqrt{898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-30\sqrt{898}}{2*-5}=\frac{-900-30\sqrt{898}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+30\sqrt{898}}{2*-5}=\frac{-900+30\sqrt{898}}{-10}
$