20r^2=13r+15

Solution for 20r^2=13r+15 equation:

20r^2=13r+15

We move all terms to the left:

20r^2-(13r+15)=0

We get rid of parentheses

20r^2-13r-15=0

a = 20; b = -13; c = -15;
Δ = b2-4ac
Δ = -132-4·20·(-15)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-37}{2*20}=\frac{-24}{40}
=-3/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+37}{2*20}=\frac{50}{40}
=1+1/4
$