24x^2+9=-33x

Solution for 24x^2+9=-33x equation:

24x^2+9=-33x

We move all terms to the left:

24x^2+9-(-33x)=0

We get rid of parentheses

24x^2+33x+9=0

a = 24; b = 33; c = +9;
Δ = b2-4ac
Δ = 332-4·24·9
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-15}{2*24}=\frac{-48}{48}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+15}{2*24}=\frac{-18}{48}
=-3/8
$