397.50=1500r2

Solution for 397.50=1500r2 equation:

397.50=1500r^2

We move all terms to the left:

397.50-(1500r^2)=0

We add all the numbers together, and all the variables

-1500r^2+397.5=0

a = -1500; b = 0; c = +397.5;
Δ = b2-4ac
Δ = 02-4·(-1500)·397.5
Δ = 2385000
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:

$\sqrt{\Delta}=\sqrt{2385000}=\sqrt{22500*106}=\sqrt{22500}*\sqrt{106}=150\sqrt{106}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{106}}{2*-1500}=\frac{0-150\sqrt{106}}{-3000}
=-\frac{150\sqrt{106}}{-3000}
=-\frac{\sqrt{106}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{106}}{2*-1500}=\frac{0+150\sqrt{106}}{-3000}
=\frac{150\sqrt{106}}{-3000}
=\frac{\sqrt{106}}{-20}
$