9x-5=1/26x-13

Solution for 9x-5=1/26x-13 equation:

9x-5=1/26x-13

We move all terms to the left:

9x-5-(1/26x-13)=0


Domain of the equation: 26x-13)!=0

x∈R


We get rid of parentheses

9x-1/26x+13-5=0

We multiply all the terms by the denominator


9x*26x+13*26x-5*26x-1=0

Wy multiply elements

234x^2+338x-130x-1=0

We add all the numbers together, and all the variables

234x^2+208x-1=0

a = 234; b = 208; c = -1;
Δ = b2-4ac
Δ = 2082-4·234·(-1)
Δ = 44200
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:

$\sqrt{\Delta}=\sqrt{44200}=\sqrt{100*442}=\sqrt{100}*\sqrt{442}=10\sqrt{442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-10\sqrt{442}}{2*234}=\frac{-208-10\sqrt{442}}{468}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+10\sqrt{442}}{2*234}=\frac{-208+10\sqrt{442}}{468}
$