367.50=(1500)(r)(2)

Solution for 367.50=(1500)(r)(2) equation:

367.50=(1500)(r)(2)

We move all terms to the left:

367.50-((1500)(r)(2))=0

determiningTheFunctionDomain
-1500r2+367.50=0

We add all the numbers together, and all the variables

-1500r^2+367.5=0

a = -1500; b = 0; c = +367.5;
Δ = b2-4ac
Δ = 02-4·(-1500)·367.5
Δ = 2205000
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:

$\sqrt{\Delta}=\sqrt{2205000}=\sqrt{1102500*2}=\sqrt{1102500}*\sqrt{2}=1050\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1050\sqrt{2}}{2*-1500}=\frac{0-1050\sqrt{2}}{-3000}
=-\frac{1050\sqrt{2}}{-3000}
=-\frac{7\sqrt{2}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1050\sqrt{2}}{2*-1500}=\frac{0+1050\sqrt{2}}{-3000}
=\frac{1050\sqrt{2}}{-3000}
=\frac{7\sqrt{2}}{-20}
$