n+n^2=342

Solution for n+n^2=342 equation:

n+n^2=342

We move all terms to the left:

n+n^2-(342)=0

a = 1; b = 1; c = -342;
Δ = b2-4ac
Δ = 12-4·1·(-342)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-37}{2*1}=\frac{-38}{2}
=-19
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+37}{2*1}=\frac{36}{2}
=18
$