5q^2+15q+5=-6

Solution for 5q^2+15q+5=-6 equation:

5q^2+15q+5=-6

We move all terms to the left:

5q^2+15q+5-(-6)=0

We add all the numbers together, and all the variables

5q^2+15q+11=0

a = 5; b = 15; c = +11;
Δ = b2-4ac
Δ = 152-4·5·11
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{5}}{2*5}=\frac{-15-\sqrt{5}}{10}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{5}}{2*5}=\frac{-15+\sqrt{5}}{10}
$