24-7/6x=3/2x

Solution for 24-7/6x=3/2x equation:

24-7/6x=3/2x

We move all terms to the left:

24-7/6x-(3/2x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7/6x-(+3/2x)+24=0

We get rid of parentheses

-7/6x-3/2x+24=0

We calculate fractions


(-14x)/12x^2+(-18x)/12x^2+24=0

We multiply all the terms by the denominator


(-14x)+(-18x)+24*12x^2=0

Wy multiply elements

288x^2+(-14x)+(-18x)=0

We get rid of parentheses

288x^2-14x-18x=0

We add all the numbers together, and all the variables

288x^2-32x=0

a = 288; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·288·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*288}=\frac{0}{576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*288}=\frac{64}{576}
=1/9
$