r^2-4r-212=0

Solution for r^2-4r-212=0 equation:

r^2-4r-212=0

a = 1; b = -4; c = -212;
Δ = b2-4ac
Δ = -42-4·1·(-212)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{6}}{2*1}=\frac{4-12\sqrt{6}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{6}}{2*1}=\frac{4+12\sqrt{6}}{2}
$