r^2=284

Solution for r^2=284 equation:

r^2=284

We move all terms to the left:

r^2-(284)=0

a = 1; b = 0; c = -284;
Δ = b2-4ac
Δ = 02-4·1·(-284)
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{71}}{2*1}=\frac{0-4\sqrt{71}}{2}
=-\frac{4\sqrt{71}}{2}
=-2\sqrt{71}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{71}}{2*1}=\frac{0+4\sqrt{71}}{2}
=\frac{4\sqrt{71}}{2}
=2\sqrt{71}
$