X+x(X-10)+x+(x-10)=100

Solution for X+x(X-10)+x+(x-10)=100 equation:

X+X(X-10)+X+(X-10)=100

We move all terms to the left:

X+X(X-10)+X+(X-10)-(100)=0

We add all the numbers together, and all the variables

2X+X(X-10)+(X-10)-100=0

We multiply parentheses

X^2+2X-10X+(X-10)-100=0

We get rid of parentheses

X^2+2X-10X+X-10-100=0

We add all the numbers together, and all the variables

X^2-7X-110=0

a = 1; b = -7; c = -110;
Δ = b2-4ac
Δ = -72-4·1·(-110)
Δ = 489
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{-(-7)-\sqrt{489}}{2*1}=\frac{7-\sqrt{489}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{489}}{2*1}=\frac{7+\sqrt{489}}{2}
$