n^2+3n-1=162

Solution for n^2+3n-1=162 equation:

n^2+3n-1=162

We move all terms to the left:

n^2+3n-1-(162)=0

We add all the numbers together, and all the variables

n^2+3n-163=0

a = 1; b = 3; c = -163;
Δ = b2-4ac
Δ = 32-4·1·(-163)
Δ = 661
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{661}}{2*1}=\frac{-3-\sqrt{661}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{661}}{2*1}=\frac{-3+\sqrt{661}}{2}
$