15r^2-6r-3=2r

Solution for 15r^2-6r-3=2r equation:

15r^2-6r-3=2r

We move all terms to the left:

15r^2-6r-3-(2r)=0

We add all the numbers together, and all the variables

15r^2-8r-3=0

a = 15; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·15·(-3)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*15}=\frac{8-2\sqrt{61}}{30}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*15}=\frac{8+2\sqrt{61}}{30}
$