5n^2=-240-70n

Solution for 5n^2=-240-70n equation:

5n^2=-240-70n

We move all terms to the left:

5n^2-(-240-70n)=0

We add all the numbers together, and all the variables

5n^2-(-70n-240)=0

We get rid of parentheses

5n^2+70n+240=0

a = 5; b = 70; c = +240;
Δ = b2-4ac
Δ = 702-4·5·240
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{-(70)-10}{2*5}=\frac{-80}{10}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10}{2*5}=\frac{-60}{10}
=-6
$