24x+9=-7x^2

Solution for 24x+9=-7x^2 equation:

24x+9=-7x^2

We move all terms to the left:

24x+9-(-7x^2)=0

We get rid of parentheses

7x^2+24x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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