5n^2=-40-30n

Solution for 5n^2=-40-30n equation:

5n^2=-40-30n

We move all terms to the left:

5n^2-(-40-30n)=0

We add all the numbers together, and all the variables

5n^2-(-30n-40)=0

We get rid of parentheses

5n^2+30n+40=0

a = 5; b = 30; c = +40;
Δ = b2-4ac
Δ = 302-4·5·40
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10}{2*5}=\frac{-40}{10}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10}{2*5}=\frac{-20}{10}
=-2
$