x+1/x-1=2.3

Solution for x+1/x-1=2.3 equation:

x+1/x-1=2.3

We move all terms to the left:

x+1/x-1-(2.3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-3.3=0

We multiply all the terms by the denominator


x*x-(3.3)*x+1=0

We multiply parentheses

x*x-3.3x+1=0

Wy multiply elements

x^2-3.3x+1=0

a = 1; b = -3.3; c = +1;
Δ = b2-4ac
Δ = -3.32-4·1·1
Δ = 6.89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3.3)-\sqrt{6.89}}{2*1}=\frac{3.3-\sqrt{6.89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.3)+\sqrt{6.89}}{2*1}=\frac{3.3+\sqrt{6.89}}{2}
$