r^2=252

Solution for r^2=252 equation:

r^2=252

We move all terms to the left:

r^2-(252)=0

a = 1; b = 0; c = -252;
Δ = b2-4ac
Δ = 02-4·1·(-252)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*1}=\frac{0-12\sqrt{7}}{2}
=-\frac{12\sqrt{7}}{2}
=-6\sqrt{7}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*1}=\frac{0+12\sqrt{7}}{2}
=\frac{12\sqrt{7}}{2}
=6\sqrt{7}
$