x^2=22x-40

Solution for x^2=22x-40 equation:

x^2=22x-40

We move all terms to the left:

x^2-(22x-40)=0

We get rid of parentheses

x^2-22x+40=0

a = 1; b = -22; c = +40;
Δ = b2-4ac
Δ = -222-4·1·40
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-18}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+18}{2*1}=\frac{40}{2}
=20
$