3q^2-5q-6=-3q^2

Solution for 3q^2-5q-6=-3q^2 equation:

3q^2-5q-6=-3q^2

We move all terms to the left:

3q^2-5q-6-(-3q^2)=0

We get rid of parentheses

3q^2+3q^2-5q-6=0

We add all the numbers together, and all the variables

6q^2-5q-6=0

a = 6; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·6·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*6}=\frac{-8}{12}
=-2/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*6}=\frac{18}{12}
=1+1/2
$