-3x^2+24x=-11

Solution for -3x^2+24x=-11 equation:

-3x^2+24x=-11

We move all terms to the left:

-3x^2+24x-(-11)=0

We add all the numbers together, and all the variables

-3x^2+24x+11=0

a = -3; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·(-3)·11
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{177}}{2*-3}=\frac{-24-2\sqrt{177}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{177}}{2*-3}=\frac{-24+2\sqrt{177}}{-6}
$