2/3*x^2=24

Solution for 2/3*x^2=24 equation:

2/3x^2=24

We move all terms to the left:

2/3x^2-(24)=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


-24*3x^2+2=0

Wy multiply elements

-72x^2+2=0

a = -72; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-72)·2
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-72}=\frac{-24}{-144}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-72}=\frac{24}{-144}
=-1/6
$