n^2-3n+8=60

Solution for n^2-3n+8=60 equation:

n^2-3n+8=60

We move all terms to the left:

n^2-3n+8-(60)=0

We add all the numbers together, and all the variables

n^2-3n-52=0

a = 1; b = -3; c = -52;
Δ = b2-4ac
Δ = -32-4·1·(-52)
Δ = 217
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{-(-3)-\sqrt{217}}{2*1}=\frac{3-\sqrt{217}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{217}}{2*1}=\frac{3+\sqrt{217}}{2}
$