X^2/3x=24/9

Solution for X^2/3x=24/9 equation:

X^2/3X=24/9

We move all terms to the left:

X^2/3X-(24/9)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X^2/3X-(+24/9)=0

We get rid of parentheses

X^2/3X-24/9=0

We calculate fractions


9X^2/27X+(-72X)/27X=0

We multiply all the terms by the denominator


9X^2+(-72X)=0

We get rid of parentheses

9X^2-72X=0

a = 9; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·9·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*9}=\frac{0}{18}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*9}=\frac{144}{18}
=8
$