x(x-20)=90=

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

x(x-20)=90=

We move all terms to the left:

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

We multiply parentheses

x^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}
$