x(x+20)=2x-20

Solution for x(x+20)=2x-20 equation:

x(x+20)=2x-20

We move all terms to the left:

x(x+20)-(2x-20)=0

We multiply parentheses

x^2+20x-(2x-20)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+18x+20=0

a = 1; b = 18; c = +20;
Δ = b2-4ac
Δ = 182-4·1·20
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{61}}{2*1}=\frac{-18-2\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{61}}{2*1}=\frac{-18+2\sqrt{61}}{2}
$