-6x^2+72x=-192

Solution for -6x^2+72x=-192 equation:

-6x^2+72x=-192

We move all terms to the left:

-6x^2+72x-(-192)=0

We add all the numbers together, and all the variables

-6x^2+72x+192=0

a = -6; b = 72; c = +192;
Δ = b2-4ac
Δ = 722-4·(-6)·192
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{17}}{2*-6}=\frac{-72-24\sqrt{17}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{17}}{2*-6}=\frac{-72+24\sqrt{17}}{-12}
$