180x^2-120=0

Solution for 180x^2-120=0 equation:

180x^2-120=0

a = 180; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·180·(-120)
Δ = 86400
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:

$\sqrt{\Delta}=\sqrt{86400}=\sqrt{14400*6}=\sqrt{14400}*\sqrt{6}=120\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{6}}{2*180}=\frac{0-120\sqrt{6}}{360}
=-\frac{120\sqrt{6}}{360}
=-\frac{\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{6}}{2*180}=\frac{0+120\sqrt{6}}{360}
=\frac{120\sqrt{6}}{360}
=\frac{\sqrt{6}}{3}
$