7n^2+n-11=-5

Solution for 7n^2+n-11=-5 equation:

7n^2+n-11=-5

We move all terms to the left:

7n^2+n-11-(-5)=0

We add all the numbers together, and all the variables

7n^2+n-6=0

a = 7; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·7·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*7}=\frac{-14}{14}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*7}=\frac{12}{14}
=6/7
$