11n^2-4n-13=-5+10n^2

Solution for 11n^2-4n-13=-5+10n^2 equation:

11n^2-4n-13=-5+10n^2

We move all terms to the left:

11n^2-4n-13-(-5+10n^2)=0

We get rid of parentheses

11n^2-10n^2-4n+5-13=0

We add all the numbers together, and all the variables

n^2-4n-8=0

a = 1; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·1·(-8)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*1}=\frac{4-4\sqrt{3}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*1}=\frac{4+4\sqrt{3}}{2}
$