7n^2-9=-18n

Solution for 7n^2-9=-18n equation:

7n^2-9=-18n

We move all terms to the left:

7n^2-9-(-18n)=0

We get rid of parentheses

7n^2+18n-9=0

a = 7; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·7·(-9)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*7}=\frac{-42}{14}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*7}=\frac{6}{14}
=3/7
$