4=-24x-3x^2-40

Solution for 4=-24x-3x^2-40 equation:

4=-24x-3x^2-40

We move all terms to the left:

4-(-24x-3x^2-40)=0

We get rid of parentheses

3x^2+24x+40+4=0

We add all the numbers together, and all the variables

3x^2+24x+44=0

a = 3; b = 24; c = +44;
Δ = b2-4ac
Δ = 242-4·3·44
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{3}}{2*3}=\frac{-24-4\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{3}}{2*3}=\frac{-24+4\sqrt{3}}{6}
$