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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 7x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


5x*7x-3x*7x-1*7x-5*7x-1-1=0

We add all the numbers together, and all the variables

5x*7x-3x*7x-1*7x-5*7x-2=0

Wy multiply elements

35x^2-21x^2-7x-35x-2=0

We add all the numbers together, and all the variables

14x^2-42x-2=0

a = 14; b = -42; c = -2;
Δ = b2-4ac
Δ = -422-4·14·(-2)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{469}}{2*14}=\frac{42-2\sqrt{469}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{469}}{2*14}=\frac{42+2\sqrt{469}}{28}
$