7n^2+13n=-6

Solution for 7n^2+13n=-6 equation:

7n^2+13n=-6

We move all terms to the left:

7n^2+13n-(-6)=0

We add all the numbers together, and all the variables

7n^2+13n+6=0

a = 7; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·7·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*7}=\frac{-14}{14}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*7}=\frac{-12}{14}
=-6/7
$