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

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

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

We move all terms to the left:

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


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

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

We get rid of parentheses

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

We calculate fractions


(3x+7)/9x^2+(-15x)/9x^2-1=0

We multiply all the terms by the denominator


(3x+7)+(-15x)-1*9x^2=0

Wy multiply elements

-9x^2+(3x+7)+(-15x)=0

We get rid of parentheses

-9x^2+3x-15x+7=0

We add all the numbers together, and all the variables

-9x^2-12x+7=0

a = -9; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-9)·7
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{11}}{2*-9}=\frac{12-6\sqrt{11}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{11}}{2*-9}=\frac{12+6\sqrt{11}}{-18}
$