180=x(4x-20)

Solution for 180=x(4x-20) equation:

180=x(4x-20)

We move all terms to the left:

180-(x(4x-20))=0


We calculate terms in parentheses: -(x(4x-20)), so:

x(4x-20)

We multiply parentheses

4x^2-20x

Back to the equation:

-(4x^2-20x)


We get rid of parentheses

-4x^2+20x+180=0

a = -4; b = 20; c = +180;
Δ = b2-4ac
Δ = 202-4·(-4)·180
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{205}}{2*-4}=\frac{-20-4\sqrt{205}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{205}}{2*-4}=\frac{-20+4\sqrt{205}}{-8}
$