5r^2-3r=15

Solution for 5r^2-3r=15 equation:

5r^2-3r=15

We move all terms to the left:

5r^2-3r-(15)=0

a = 5; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·5·(-15)
Δ = 309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{309}}{2*5}=\frac{3-\sqrt{309}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{309}}{2*5}=\frac{3+\sqrt{309}}{10}
$