5n^2=-90-45n

Solution for 5n^2=-90-45n equation:

5n^2=-90-45n

We move all terms to the left:

5n^2-(-90-45n)=0

We add all the numbers together, and all the variables

5n^2-(-45n-90)=0

We get rid of parentheses

5n^2+45n+90=0

a = 5; b = 45; c = +90;
Δ = b2-4ac
Δ = 452-4·5·90
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-15}{2*5}=\frac{-60}{10}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+15}{2*5}=\frac{-30}{10}
=-3
$