8x=x^2/3

Solution for 8x=x^2/3 equation:

8x=x^2/3

We move all terms to the left:

8x-(x^2/3)=0

We get rid of parentheses

-x^2/3+8x=0

We multiply all the terms by the denominator


-x^2+8x*3=0

We add all the numbers together, and all the variables

-1x^2+8x*3=0

Wy multiply elements

-1x^2+24x=0

a = -1; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-1)·0
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{-(24)-24}{2*-1}=\frac{-48}{-2}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-1}=\frac{0}{-2}
=0
$