X2-21x+100=x+1

Solution for X2-21x+100=x+1 equation:

X2-21X+100=X+1

We move all terms to the left:

X2-21X+100-(X+1)=0

We add all the numbers together, and all the variables

X^2-21X-(X+1)+100=0

We get rid of parentheses

X^2-21X-X-1+100=0

We add all the numbers together, and all the variables

X^2-22X+99=0

a = 1; b = -22; c = +99;
Δ = b2-4ac
Δ = -222-4·1·99
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{22}}{2*1}=\frac{22-2\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{22}}{2*1}=\frac{22+2\sqrt{22}}{2}
$