400-12x^2=0

Solution for 400-12x^2=0 equation:

400-12x^2=0

a = -12; b = 0; c = +400;
Δ = b2-4ac
Δ = 02-4·(-12)·400
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*-12}=\frac{0-80\sqrt{3}}{-24}
=-\frac{80\sqrt{3}}{-24}
=-\frac{10\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*-12}=\frac{0+80\sqrt{3}}{-24}
=\frac{80\sqrt{3}}{-24}
=\frac{10\sqrt{3}}{-3}
$