7+9n=-2n^2

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

7+9n=-2n^2

We move all terms to the left:

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

We get rid of parentheses

2n^2+9n+7=0

a = 2; b = 9; c = +7;
Δ = b2-4ac
Δ = 92-4·2·7
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*2}=\frac{-14}{4}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*2}=\frac{-4}{4}
=-1
$