6n^2-6=-9n

Solution for 6n^2-6=-9n equation:

6n^2-6=-9n

We move all terms to the left:

6n^2-6-(-9n)=0

We get rid of parentheses

6n^2+9n-6=0

a = 6; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·6·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*6}=\frac{-24}{12}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*6}=\frac{6}{12}
=1/2
$