2/3x^2-16=32

Solution for 2/3x^2-16=32 equation:

2/3x^2-16=32

We move all terms to the left:

2/3x^2-16-(32)=0


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

x^2!=0/3

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x^2-48=0

We multiply all the terms by the denominator


-48*3x^2+2=0

Wy multiply elements

-144x^2+2=0

a = -144; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-144)·2
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-144}=\frac{0-24\sqrt{2}}{-288}
=-\frac{24\sqrt{2}}{-288}
=-\frac{\sqrt{2}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-144}=\frac{0+24\sqrt{2}}{-288}
=\frac{24\sqrt{2}}{-288}
=\frac{\sqrt{2}}{-12}
$