9r=-6r^2-3

Solution for 9r=-6r^2-3 equation:

9r=-6r^2-3

We move all terms to the left:

9r-(-6r^2-3)=0

We get rid of parentheses

6r^2+9r+3=0

a = 6; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·6·3
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*6}=\frac{-12}{12}
=-1
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*6}=\frac{-6}{12}
=-1/2
$