r^2-12r=8

Solution for r^2-12r=8 equation:

r^2-12r=8

We move all terms to the left:

r^2-12r-(8)=0

a = 1; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·1·(-8)
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{-(-12)-4\sqrt{11}}{2*1}=\frac{12-4\sqrt{11}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{11}}{2*1}=\frac{12+4\sqrt{11}}{2}
$