2x-(7-5x)/9x-(3+4x)=6/7

Solution for 2x-(7-5x)/9x-(3+4x)=6/7 equation:

2x-(7-5x)/9x-(3+4x)=6/7

We move all terms to the left:

2x-(7-5x)/9x-(3+4x)-(6/7)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(-5x+7)/9x-(4x+3)-(+6/7)=0

We get rid of parentheses

2x-(-5x+7)/9x-4x-3-6/7=0

We calculate fractions


2x-4x+(35x-49)/63x+(-54x)/63x-3=0

We add all the numbers together, and all the variables

-2x+(35x-49)/63x+(-54x)/63x-3=0

We multiply all the terms by the denominator


-2x*63x+(35x-49)+(-54x)-3*63x=0

Wy multiply elements

-126x^2+(35x-49)+(-54x)-189x=0

We get rid of parentheses

-126x^2+35x-54x-189x-49=0

We add all the numbers together, and all the variables

-126x^2-208x-49=0

a = -126; b = -208; c = -49;
Δ = b2-4ac
Δ = -2082-4·(-126)·(-49)
Δ = 18568
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:

$\sqrt{\Delta}=\sqrt{18568}=\sqrt{4*4642}=\sqrt{4}*\sqrt{4642}=2\sqrt{4642}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-2\sqrt{4642}}{2*-126}=\frac{208-2\sqrt{4642}}{-252}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+2\sqrt{4642}}{2*-126}=\frac{208+2\sqrt{4642}}{-252}
$