14n+20=-n2

Solution for 14n+20=-n2 equation:

14n+20=-n2

We move all terms to the left:

14n+20-(-n2)=0

We add all the numbers together, and all the variables

-(-1n^2)+14n+20=0

We get rid of parentheses

1n^2+14n+20=0

We add all the numbers together, and all the variables

n^2+14n+20=0

a = 1; b = 14; c = +20;
Δ = b2-4ac
Δ = 142-4·1·20
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{29}}{2*1}=\frac{-14-2\sqrt{29}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{29}}{2*1}=\frac{-14+2\sqrt{29}}{2}
$