792x^2+97=180

Solution for 792x^2+97=180 equation:

792x^2+97=180

We move all terms to the left:

792x^2+97-(180)=0

We add all the numbers together, and all the variables

792x^2-83=0

a = 792; b = 0; c = -83;
Δ = b2-4ac
Δ = 02-4·792·(-83)
Δ = 262944
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:

$\sqrt{\Delta}=\sqrt{262944}=\sqrt{144*1826}=\sqrt{144}*\sqrt{1826}=12\sqrt{1826}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{1826}}{2*792}=\frac{0-12\sqrt{1826}}{1584}
=-\frac{12\sqrt{1826}}{1584}
=-\frac{\sqrt{1826}}{132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{1826}}{2*792}=\frac{0+12\sqrt{1826}}{1584}
=\frac{12\sqrt{1826}}{1584}
=\frac{\sqrt{1826}}{132}
$