n^2+14n=-37

Solution for n^2+14n=-37 equation:

n^2+14n=-37

We move all terms to the left:

n^2+14n-(-37)=0

We add all the numbers together, and all the variables

n^2+14n+37=0

a = 1; b = 14; c = +37;
Δ = b2-4ac
Δ = 142-4·1·37
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{3}}{2*1}=\frac{-14-4\sqrt{3}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{3}}{2*1}=\frac{-14+4\sqrt{3}}{2}
$