3x-1=1/210x-26

Solution for 3x-1=1/210x-26 equation:

3x-1=1/210x-26

We move all terms to the left:

3x-1-(1/210x-26)=0


Domain of the equation: 210x-26)!=0

x∈R


We get rid of parentheses

3x-1/210x+26-1=0

We multiply all the terms by the denominator


3x*210x+26*210x-1*210x-1=0

Wy multiply elements

630x^2+5460x-210x-1=0

We add all the numbers together, and all the variables

630x^2+5250x-1=0

a = 630; b = 5250; c = -1;
Δ = b2-4ac
Δ = 52502-4·630·(-1)
Δ = 27565020
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:

$\sqrt{\Delta}=\sqrt{27565020}=\sqrt{36*765695}=\sqrt{36}*\sqrt{765695}=6\sqrt{765695}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5250)-6\sqrt{765695}}{2*630}=\frac{-5250-6\sqrt{765695}}{1260}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5250)+6\sqrt{765695}}{2*630}=\frac{-5250+6\sqrt{765695}}{1260}
$