(X-20)(x-20)=x*18

Solution for (X-20)(x-20)=x*18 equation:

(X-20)(X-20)=X*18

We move all terms to the left:

(X-20)(X-20)-(X*18)=0

We add all the numbers together, and all the variables

(X-20)(X-20)-(+X*18)=0

We get rid of parentheses

(X-20)(X-20)-X*18=0

We multiply parentheses ..

(+X^2-20X-20X+400)-X*18=0

Wy multiply elements

(+X^2-20X-20X+400)-18X=0

We get rid of parentheses

X^2-20X-20X-18X+400=0

We add all the numbers together, and all the variables

X^2-58X+400=0

a = 1; b = -58; c = +400;
Δ = b2-4ac
Δ = -582-4·1·400
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-42}{2*1}=\frac{16}{2}
=8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+42}{2*1}=\frac{100}{2}
=50
$