X+x(x-20)=50

Solution for X+x(x-20)=50 equation:

X+X(X-20)=50

We move all terms to the left:

X+X(X-20)-(50)=0

We multiply parentheses

X^2+X-20X-50=0

We add all the numbers together, and all the variables

X^2-19X-50=0

a = 1; b = -19; c = -50;
Δ = b2-4ac
Δ = -192-4·1·(-50)
Δ = 561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{561}}{2*1}=\frac{19-\sqrt{561}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{561}}{2*1}=\frac{19+\sqrt{561}}{2}
$