3^2+30=r^2

Solution for 3^2+30=r^2 equation:

3^2+30=r^2

We move all terms to the left:

3^2+30-(r^2)=0

We add all the numbers together, and all the variables

-1r^2+39=0

a = -1; b = 0; c = +39;
Δ = b2-4ac
Δ = 02-4·(-1)·39
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{39}}{2*-1}=\frac{0-2\sqrt{39}}{-2}
=-\frac{2\sqrt{39}}{-2}
=-\frac{\sqrt{39}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{39}}{2*-1}=\frac{0+2\sqrt{39}}{-2}
=\frac{2\sqrt{39}}{-2}
=\frac{\sqrt{39}}{-1}
$