x^2=6x+22

Solution for x^2=6x+22 equation:

x^2=6x+22

We move all terms to the left:

x^2-(6x+22)=0

We get rid of parentheses

x^2-6x-22=0

a = 1; b = -6; c = -22;
Δ = b2-4ac
Δ = -62-4·1·(-22)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{31}}{2*1}=\frac{6-2\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{31}}{2*1}=\frac{6+2\sqrt{31}}{2}
$