-36x^2-68x^2+972=0

Solution for -36x^2-68x^2+972=0 equation:

-36x^2-68x^2+972=0

We add all the numbers together, and all the variables

-104x^2+972=0

a = -104; b = 0; c = +972;
Δ = b2-4ac
Δ = 02-4·(-104)·972
Δ = 404352
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:

$\sqrt{\Delta}=\sqrt{404352}=\sqrt{5184*78}=\sqrt{5184}*\sqrt{78}=72\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{78}}{2*-104}=\frac{0-72\sqrt{78}}{-208}
=-\frac{72\sqrt{78}}{-208}
=-\frac{9\sqrt{78}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{78}}{2*-104}=\frac{0+72\sqrt{78}}{-208}
=\frac{72\sqrt{78}}{-208}
=\frac{9\sqrt{78}}{-26}
$