-36x^2+192-144=0

Solution for -36x^2+192-144=0 equation:

-36x^2+192-144=0

We add all the numbers together, and all the variables

-36x^2+48=0

a = -36; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-36)·48
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*-36}=\frac{0-48\sqrt{3}}{-72}
=-\frac{48\sqrt{3}}{-72}
=-\frac{2\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*-36}=\frac{0+48\sqrt{3}}{-72}
=\frac{48\sqrt{3}}{-72}
=\frac{2\sqrt{3}}{-3}
$