7n^2+84n+240=-5

Solution for 7n^2+84n+240=-5 equation:

7n^2+84n+240=-5

We move all terms to the left:

7n^2+84n+240-(-5)=0

We add all the numbers together, and all the variables

7n^2+84n+245=0

a = 7; b = 84; c = +245;
Δ = b2-4ac
Δ = 842-4·7·245
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-14}{2*7}=\frac{-98}{14}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+14}{2*7}=\frac{-70}{14}
=-5
$