4n^2-8n=11

Solution for 4n^2-8n=11 equation:

4n^2-8n=11

We move all terms to the left:

4n^2-8n-(11)=0

a = 4; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·4·(-11)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*4}=\frac{8-4\sqrt{15}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*4}=\frac{8+4\sqrt{15}}{8}
$