X=x^2-22x+21

Solution for X=x^2-22x+21 equation:

X=X^2-22X+21

We move all terms to the left:

X-(X^2-22X+21)=0

We get rid of parentheses

-X^2+X+22X-21=0

We add all the numbers together, and all the variables

-1X^2+23X-21=0

a = -1; b = 23; c = -21;
Δ = b2-4ac
Δ = 232-4·(-1)·(-21)
Δ = 445
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{-(23)-\sqrt{445}}{2*-1}=\frac{-23-\sqrt{445}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{445}}{2*-1}=\frac{-23+\sqrt{445}}{-2}
$