x^2+36=22x

Solution for x^2+36=22x equation:

x^2+36=22x

We move all terms to the left:

x^2+36-(22x)=0

a = 1; b = -22; c = +36;
Δ = b2-4ac
Δ = -222-4·1·36
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{85}}{2*1}=\frac{22-2\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{85}}{2*1}=\frac{22+2\sqrt{85}}{2}
$