2x+1=27/x-1

Solution for 2x+1=27/x-1 equation:

2x+1=27/x-1

We move all terms to the left:

2x+1-(27/x-1)=0


Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

2x-27/x+1+1=0

We multiply all the terms by the denominator


2x*x+1*x+1*x-27=0

We add all the numbers together, and all the variables

2x+2x*x-27=0

Wy multiply elements

2x^2+2x-27=0

a = 2; b = 2; c = -27;
Δ = b2-4ac
Δ = 22-4·2·(-27)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*2}=\frac{-2-2\sqrt{55}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*2}=\frac{-2+2\sqrt{55}}{4}
$