4/7x=28-2/3x

Solution for 4/7x=28-2/3x equation:

4/7x=28-2/3x

We move all terms to the left:

4/7x-(28-2/3x)=0


Domain of the equation: 7x!=0

x!=0/7

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

4/7x-(-2/3x+28)=0

We get rid of parentheses

4/7x+2/3x-28=0

We calculate fractions


12x/21x^2+14x/21x^2-28=0

We multiply all the terms by the denominator


12x+14x-28*21x^2=0

We add all the numbers together, and all the variables

26x-28*21x^2=0

Wy multiply elements

-588x^2+26x=0

a = -588; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-588)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-588}=\frac{-52}{-1176}
=13/294
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-588}=\frac{0}{-1176}
=0
$