24x^2+11=-33x

Solution for 24x^2+11=-33x equation:

24x^2+11=-33x

We move all terms to the left:

24x^2+11-(-33x)=0

We get rid of parentheses

24x^2+33x+11=0

a = 24; b = 33; c = +11;
Δ = b2-4ac
Δ = 332-4·24·11
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{33}}{2*24}=\frac{-33-\sqrt{33}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{33}}{2*24}=\frac{-33+\sqrt{33}}{48}
$