x^2=16/192

Solution for x^2=16/192 equation:

x^2=16/192

We move all terms to the left:

x^2-(16/192)=0

We add all the numbers together, and all the variables

x^2-(+16/192)=0

We get rid of parentheses

x^2-16/192=0

We multiply all the terms by the denominator


x^2*192-16=0

Wy multiply elements

192x^2-16=0

a = 192; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·192·(-16)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*192}=\frac{0-64\sqrt{3}}{384}
=-\frac{64\sqrt{3}}{384}
=-\frac{\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*192}=\frac{0+64\sqrt{3}}{384}
=\frac{64\sqrt{3}}{384}
=\frac{\sqrt{3}}{6}
$