180x^2-24=0

Solution for 180x^2-24=0 equation:

180x^2-24=0

a = 180; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·180·(-24)
Δ = 17280
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:

$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{30}}{2*180}=\frac{0-24\sqrt{30}}{360}
=-\frac{24\sqrt{30}}{360}
=-\frac{\sqrt{30}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{30}}{2*180}=\frac{0+24\sqrt{30}}{360}
=\frac{24\sqrt{30}}{360}
=\frac{\sqrt{30}}{15}
$