9n^2+189=-90n

Solution for 9n^2+189=-90n equation:

9n^2+189=-90n

We move all terms to the left:

9n^2+189-(-90n)=0

We get rid of parentheses

9n^2+90n+189=0

a = 9; b = 90; c = +189;
Δ = b2-4ac
Δ = 902-4·9·189
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-36}{2*9}=\frac{-126}{18}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+36}{2*9}=\frac{-54}{18}
=-3
$