5x-3=1/7x-3

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

5x-3=1/7x-3

We move all terms to the left:

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


Domain of the equation: 7x-3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

35x^2+21x-21x-1=0

We add all the numbers together, and all the variables

35x^2-1=0

a = 35; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·35·(-1)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*35}=\frac{0-2\sqrt{35}}{70}
=-\frac{2\sqrt{35}}{70}
=-\frac{\sqrt{35}}{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*35}=\frac{0+2\sqrt{35}}{70}
=\frac{2\sqrt{35}}{70}
=\frac{\sqrt{35}}{35}
$