n^2-4n=61

Solution for n^2-4n=61 equation:

n^2-4n=61

We move all terms to the left:

n^2-4n-(61)=0

a = 1; b = -4; c = -61;
Δ = b2-4ac
Δ = -42-4·1·(-61)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{65}}{2*1}=\frac{4-2\sqrt{65}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{65}}{2*1}=\frac{4+2\sqrt{65}}{2}
$