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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(5x+7)/15x^2+(-9x)/15x^2-3=0

We multiply all the terms by the denominator


(5x+7)+(-9x)-3*15x^2=0

Wy multiply elements

-45x^2+(5x+7)+(-9x)=0

We get rid of parentheses

-45x^2+5x-9x+7=0

We add all the numbers together, and all the variables

-45x^2-4x+7=0

a = -45; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-45)·7
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{319}}{2*-45}=\frac{4-2\sqrt{319}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{319}}{2*-45}=\frac{4+2\sqrt{319}}{-90}
$