32-6x^2=0

Solution for 32-6x^2=0 equation:

32-6x^2=0

a = -6; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-6)·32
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*-6}=\frac{0-16\sqrt{3}}{-12}
=-\frac{16\sqrt{3}}{-12}
=-\frac{4\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*-6}=\frac{0+16\sqrt{3}}{-12}
=\frac{16\sqrt{3}}{-12}
=\frac{4\sqrt{3}}{-3}
$