r^2-93=12r

Solution for r^2-93=12r equation:

r^2-93=12r

We move all terms to the left:

r^2-93-(12r)=0

a = 1; b = -12; c = -93;
Δ = b2-4ac
Δ = -122-4·1·(-93)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{129}}{2*1}=\frac{12-2\sqrt{129}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{129}}{2*1}=\frac{12+2\sqrt{129}}{2}
$