3n^2+7n+11=n^2-8n-7

Solution for 3n^2+7n+11=n^2-8n-7 equation:

3n^2+7n+11=n^2-8n-7

We move all terms to the left:

3n^2+7n+11-(n^2-8n-7)=0

We get rid of parentheses

3n^2-n^2+7n+8n+7+11=0

We add all the numbers together, and all the variables

2n^2+15n+18=0

a = 2; b = 15; c = +18;
Δ = b2-4ac
Δ = 152-4·2·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*2}=\frac{-24}{4}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*2}=\frac{-6}{4}
=-1+1/2
$