5n^2=-45n-70

Solution for 5n^2=-45n-70 equation:

5n^2=-45n-70

We move all terms to the left:

5n^2-(-45n-70)=0

We get rid of parentheses

5n^2+45n+70=0

a = 5; b = 45; c = +70;
Δ = b2-4ac
Δ = 452-4·5·70
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-25}{2*5}=\frac{-70}{10}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+25}{2*5}=\frac{-20}{10}
=-2
$