-n^2-11n=2-4n^2-3n

Solution for -n^2-11n=2-4n^2-3n equation:

-n^2-11n=2-4n^2-3n

We move all terms to the left:

-n^2-11n-(2-4n^2-3n)=0

We add all the numbers together, and all the variables

-1n^2-(2-4n^2-3n)-11n=0

We get rid of parentheses

-1n^2+4n^2+3n-11n-2=0

We add all the numbers together, and all the variables

3n^2-8n-2=0

a = 3; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·3·(-2)
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*3}=\frac{8-2\sqrt{22}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*3}=\frac{8+2\sqrt{22}}{6}
$