7n^2-6=-11n

Solution for 7n^2-6=-11n equation:

7n^2-6=-11n

We move all terms to the left:

7n^2-6-(-11n)=0

We get rid of parentheses

7n^2+11n-6=0

a = 7; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·7·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-17}{2*7}=\frac{-28}{14}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+17}{2*7}=\frac{6}{14}
=3/7
$