6q2+13q=-6

Solution for 6q2+13q=-6 equation:

6q^2+13q=-6

We move all terms to the left:

6q^2+13q-(-6)=0

We add all the numbers together, and all the variables

6q^2+13q+6=0

a = 6; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·6·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*6}=\frac{-18}{12}
=-1+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*6}=\frac{-8}{12}
=-2/3
$