3/4x-1/2=5/12x

Solution for 3/4x-1/2=5/12x equation:

3/4x-1/2=5/12x

We move all terms to the left:

3/4x-1/2-(5/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+5/12x)-1/2=0

We get rid of parentheses

3/4x-5/12x-1/2=0

We calculate fractions


(-48x^2)/192x^2+144x/192x^2+(-80x)/192x^2=0

We multiply all the terms by the denominator


(-48x^2)+144x+(-80x)=0

We get rid of parentheses

-48x^2+144x-80x=0

We add all the numbers together, and all the variables

-48x^2+64x=0

a = -48; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-48)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-48}=\frac{-128}{-96}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-48}=\frac{0}{-96}
=0
$