13x-1=13/9x+27

Solution for 13x-1=13/9x+27 equation:

13x-1=13/9x+27

We move all terms to the left:

13x-1-(13/9x+27)=0


Domain of the equation: 9x+27)!=0

x∈R


We get rid of parentheses

13x-13/9x-27-1=0

We multiply all the terms by the denominator


13x*9x-27*9x-1*9x-13=0

Wy multiply elements

117x^2-243x-9x-13=0

We add all the numbers together, and all the variables

117x^2-252x-13=0

a = 117; b = -252; c = -13;
Δ = b2-4ac
Δ = -2522-4·117·(-13)
Δ = 69588
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:

$\sqrt{\Delta}=\sqrt{69588}=\sqrt{36*1933}=\sqrt{36}*\sqrt{1933}=6\sqrt{1933}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-6\sqrt{1933}}{2*117}=\frac{252-6\sqrt{1933}}{234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+6\sqrt{1933}}{2*117}=\frac{252+6\sqrt{1933}}{234}
$