24-1/2x=1/3x

Solution for 24-1/2x=1/3x equation:

24-1/2x=1/3x

We move all terms to the left:

24-1/2x-(1/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(+1/3x)+24=0

We get rid of parentheses

-1/2x-1/3x+24=0

We calculate fractions


(-3x)/6x^2+(-2x)/6x^2+24=0

We multiply all the terms by the denominator


(-3x)+(-2x)+24*6x^2=0

Wy multiply elements

144x^2+(-3x)+(-2x)=0

We get rid of parentheses

144x^2-3x-2x=0

We add all the numbers together, and all the variables

144x^2-5x=0

a = 144; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·144·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*144}=\frac{0}{288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*144}=\frac{10}{288}
=5/144
$