427.50=1500(r)(2)

Solution for 427.50=1500(r)(2) equation:

427.50=1500(r)(2)

We move all terms to the left:

427.50-(1500(r)(2))=0

determiningTheFunctionDomain
-1500r2+427.50=0

We add all the numbers together, and all the variables

-1500r^2+427.5=0

a = -1500; b = 0; c = +427.5;
Δ = b2-4ac
Δ = 02-4·(-1500)·427.5
Δ = 2565000
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:

$\sqrt{\Delta}=\sqrt{2565000}=\sqrt{22500*114}=\sqrt{22500}*\sqrt{114}=150\sqrt{114}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{114}}{2*-1500}=\frac{0-150\sqrt{114}}{-3000}
=-\frac{150\sqrt{114}}{-3000}
=-\frac{\sqrt{114}}{-20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{114}}{2*-1500}=\frac{0+150\sqrt{114}}{-3000}
=\frac{150\sqrt{114}}{-3000}
=\frac{\sqrt{114}}{-20}
$