7/4x+1/3x=1+5/3x

Solution for 7/4x+1/3x=1+5/3x equation:

7/4x+1/3x=1+5/3x

We move all terms to the left:

7/4x+1/3x-(1+5/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

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

7/4x+1/3x-(5/3x+1)=0

We get rid of parentheses

7/4x+1/3x-5/3x-1=0

We calculate fractions


21x/12x^2+(-20x+1)/12x^2-1=0

We multiply all the terms by the denominator


21x+(-20x+1)-1*12x^2=0

Wy multiply elements

-12x^2+21x+(-20x+1)=0

We get rid of parentheses

-12x^2+21x-20x+1=0

We add all the numbers together, and all the variables

-12x^2+x+1=0

a = -12; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-12)·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-12}=\frac{-8}{-24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-12}=\frac{6}{-24}
=-1/4
$