n^2-14n=52

Solution for n^2-14n=52 equation:

n^2-14n=52

We move all terms to the left:

n^2-14n-(52)=0

a = 1; b = -14; c = -52;
Δ = b2-4ac
Δ = -142-4·1·(-52)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{101}}{2*1}=\frac{14-2\sqrt{101}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{101}}{2*1}=\frac{14+2\sqrt{101}}{2}
$