n^2-7n-61=-9

Solution for n^2-7n-61=-9 equation:

n^2-7n-61=-9

We move all terms to the left:

n^2-7n-61-(-9)=0

We add all the numbers together, and all the variables

n^2-7n-52=0

a = 1; b = -7; c = -52;
Δ = b2-4ac
Δ = -72-4·1·(-52)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{257}}{2*1}=\frac{7-\sqrt{257}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{257}}{2*1}=\frac{7+\sqrt{257}}{2}
$