2/3x^2-16=0

Solution for 2/3x^2-16=0 equation:

2/3x^2-16=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-16*3x^2+2=0

Wy multiply elements

-48x^2+2=0

a = -48; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-48)·2
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*-48}=\frac{0-8\sqrt{6}}{-96}
=-\frac{8\sqrt{6}}{-96}
=-\frac{\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*-48}=\frac{0+8\sqrt{6}}{-96}
=\frac{8\sqrt{6}}{-96}
=\frac{\sqrt{6}}{-12}
$