4n^2-13=2n

Solution for 4n^2-13=2n equation:

4n^2-13=2n

We move all terms to the left:

4n^2-13-(2n)=0

a = 4; b = -2; c = -13;
Δ = b2-4ac
Δ = -22-4·4·(-13)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{53}}{2*4}=\frac{2-2\sqrt{53}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{53}}{2*4}=\frac{2+2\sqrt{53}}{8}
$