90=x(x-20)

Solution for 90=x(x-20) equation:

90=x(x-20)

We move all terms to the left:

90-(x(x-20))=0


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

x(x-20)

We multiply parentheses

x^2-20x

Back to the equation:

-(x^2-20x)


We get rid of parentheses

-x^2+20x+90=0

We add all the numbers together, and all the variables

-1x^2+20x+90=0

a = -1; b = 20; c = +90;
Δ = b2-4ac
Δ = 202-4·(-1)·90
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{190}}{2*-1}=\frac{-20-2\sqrt{190}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{190}}{2*-1}=\frac{-20+2\sqrt{190}}{-2}
$