-3x^2-24x+17=40

Solution for -3x^2-24x+17=40 equation:

-3x^2-24x+17=40

We move all terms to the left:

-3x^2-24x+17-(40)=0

We add all the numbers together, and all the variables

-3x^2-24x-23=0

a = -3; b = -24; c = -23;
Δ = b2-4ac
Δ = -242-4·(-3)·(-23)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{3}}{2*-3}=\frac{24-10\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{3}}{2*-3}=\frac{24+10\sqrt{3}}{-6}
$