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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


9x/15x^2+(-35x+1)/15x^2-7=0

We multiply all the terms by the denominator


9x+(-35x+1)-7*15x^2=0

Wy multiply elements

-105x^2+9x+(-35x+1)=0

We get rid of parentheses

-105x^2+9x-35x+1=0

We add all the numbers together, and all the variables

-105x^2-26x+1=0

a = -105; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·(-105)·1
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{274}}{2*-105}=\frac{26-2\sqrt{274}}{-210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{274}}{2*-105}=\frac{26+2\sqrt{274}}{-210}
$