117x^2-324=0

Solution for 117x^2-324=0 equation:

117x^2-324=0

a = 117; b = 0; c = -324;
Δ = b2-4ac
Δ = 02-4·117·(-324)
Δ = 151632
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:

$\sqrt{\Delta}=\sqrt{151632}=\sqrt{11664*13}=\sqrt{11664}*\sqrt{13}=108\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108\sqrt{13}}{2*117}=\frac{0-108\sqrt{13}}{234}
=-\frac{108\sqrt{13}}{234}
=-\frac{6\sqrt{13}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108\sqrt{13}}{2*117}=\frac{0+108\sqrt{13}}{234}
=\frac{108\sqrt{13}}{234}
=\frac{6\sqrt{13}}{13}
$