n2+17n=-30

Solution for n2+17n=-30 equation:

n2+17n=-30

We move all terms to the left:

n2+17n-(-30)=0

We add all the numbers together, and all the variables

n^2+17n+30=0

a = 1; b = 17; c = +30;
Δ = b2-4ac
Δ = 172-4·1·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-13}{2*1}=\frac{-30}{2}
=-15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*1}=\frac{-4}{2}
=-2
$