(n^2-12)+(4n+11)=76

Solution for (n^2-12)+(4n+11)=76 equation:

(n^2-12)+(4n+11)=76

We move all terms to the left:

(n^2-12)+(4n+11)-(76)=0

We get rid of parentheses

n^2+4n-12+11-76=0

We add all the numbers together, and all the variables

n^2+4n-77=0

a = 1; b = 4; c = -77;
Δ = b2-4ac
Δ = 42-4·1·(-77)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-18}{2*1}=\frac{-22}{2}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+18}{2*1}=\frac{14}{2}
=7
$