n^2+3n+4=60

Solution for n^2+3n+4=60 equation:

n^2+3n+4=60

We move all terms to the left:

n^2+3n+4-(60)=0

We add all the numbers together, and all the variables

n^2+3n-56=0

a = 1; b = 3; c = -56;
Δ = b2-4ac
Δ = 32-4·1·(-56)
Δ = 233
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{233}}{2*1}=\frac{-3-\sqrt{233}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{233}}{2*1}=\frac{-3+\sqrt{233}}{2}
$