x2-8x-22=6

Solution for x2-8x-22=6 equation:

x2-8x-22=6

We move all terms to the left:

x2-8x-22-(6)=0

We add all the numbers together, and all the variables

x^2-8x-28=0

a = 1; b = -8; c = -28;
Δ = b2-4ac
Δ = -82-4·1·(-28)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{11}}{2*1}=\frac{8-4\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{11}}{2*1}=\frac{8+4\sqrt{11}}{2}
$