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 get rid of parentheses

15r^2-6r+2r-3=0

We add all the numbers together, and all the variables

15r^2-4r-3=0

a = 15; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·15·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*15}=\frac{-10}{30}
=-1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*15}=\frac{18}{30}
=3/5
$