X^2+22x=x+100

Solution for X^2+22x=x+100 equation:

X^2+22X=X+100

We move all terms to the left:

X^2+22X-(X+100)=0

We get rid of parentheses

X^2+22X-X-100=0

We add all the numbers together, and all the variables

X^2+21X-100=0

a = 1; b = 21; c = -100;
Δ = b2-4ac
Δ = 212-4·1·(-100)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-29}{2*1}=\frac{-50}{2}
=-25
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+29}{2*1}=\frac{8}{2}
=4
$