r^2-8r-22=6

Solution for r^2-8r-22=6 equation:

r^2-8r-22=6

We move all terms to the left:

r^2-8r-22-(6)=0

We add all the numbers together, and all the variables

r^2-8r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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