4/3x-7/4=5/6x

Solution for 4/3x-7/4=5/6x equation:

4/3x-7/4=5/6x

We move all terms to the left:

4/3x-7/4-(5/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(+5/6x)-7/4=0

We get rid of parentheses

4/3x-5/6x-7/4=0

We calculate fractions


(-756x^2)/288x^2+384x/288x^2+(-240x)/288x^2=0

We multiply all the terms by the denominator


(-756x^2)+384x+(-240x)=0

We get rid of parentheses

-756x^2+384x-240x=0

We add all the numbers together, and all the variables

-756x^2+144x=0

a = -756; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-756)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-756}=\frac{-288}{-1512}
=4/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-756}=\frac{0}{-1512}
=0
$