x(x-10)=22

Solution for x(x-10)=22 equation:

x(x-10)=22

We move all terms to the left:

x(x-10)-(22)=0

We multiply parentheses

x^2-10x-22=0

a = 1; b = -10; c = -22;
Δ = b2-4ac
Δ = -102-4·1·(-22)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{47}}{2*1}=\frac{10-2\sqrt{47}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{47}}{2*1}=\frac{10+2\sqrt{47}}{2}
$