15n^2+70n=-40

Solution for 15n^2+70n=-40 equation:

15n^2+70n=-40

We move all terms to the left:

15n^2+70n-(-40)=0

We add all the numbers together, and all the variables

15n^2+70n+40=0

a = 15; b = 70; c = +40;
Δ = b2-4ac
Δ = 702-4·15·40
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-50}{2*15}=\frac{-120}{30}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+50}{2*15}=\frac{-20}{30}
=-2/3
$