15r2+15=3+6r2+39r

Solution for 15r2+15=3+6r2+39r equation:

15r^2+15=3+6r^2+39r

We move all terms to the left:

15r^2+15-(3+6r^2+39r)=0

We get rid of parentheses

15r^2-6r^2-39r-3+15=0

We add all the numbers together, and all the variables

9r^2-39r+12=0

a = 9; b = -39; c = +12;
Δ = b2-4ac
Δ = -392-4·9·12
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-33}{2*9}=\frac{6}{18}
=1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+33}{2*9}=\frac{72}{18}
=4
$