-24n=-9-7n^2

Solution for -24n=-9-7n^2 equation:

-24n=-9-7n^2

We move all terms to the left:

-24n-(-9-7n^2)=0

We get rid of parentheses

7n^2-24n+9=0

a = 7; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·7·9
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*7}=\frac{6}{14}
=3/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*7}=\frac{42}{14}
=3
$