6(72x^2-150)=0

Solution for 6(72x^2-150)=0 equation:

6(72x^2-150)=0

We multiply parentheses

432x^2-900=0

a = 432; b = 0; c = -900;
Δ = b2-4ac
Δ = 02-4·432·(-900)
Δ = 1555200
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:

$\sqrt{\Delta}=\sqrt{1555200}=\sqrt{518400*3}=\sqrt{518400}*\sqrt{3}=720\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-720\sqrt{3}}{2*432}=\frac{0-720\sqrt{3}}{864}
=-\frac{720\sqrt{3}}{864}
=-\frac{5\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+720\sqrt{3}}{2*432}=\frac{0+720\sqrt{3}}{864}
=\frac{720\sqrt{3}}{864}
=\frac{5\sqrt{3}}{6}
$