r^2-41=-12r

Solution for r^2-41=-12r equation:

r^2-41=-12r

We move all terms to the left:

r^2-41-(-12r)=0

We get rid of parentheses

r^2+12r-41=0

a = 1; b = 12; c = -41;
Δ = b2-4ac
Δ = 122-4·1·(-41)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{77}}{2*1}=\frac{-12-2\sqrt{77}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{77}}{2*1}=\frac{-12+2\sqrt{77}}{2}
$