x=3.46-1/x

Solution for x=3.46-1/x equation:

x=3.46-1/x

We move all terms to the left:

x-(3.46-1/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-1/x+3.46)=0

We get rid of parentheses

x+1/x-3.46=0

We multiply all the terms by the denominator


x*x-(3.46)*x+1=0

We multiply parentheses

x*x-3.46x+1=0

Wy multiply elements

x^2-3.46x+1=0

a = 1; b = -3.46; c = +1;
Δ = b2-4ac
Δ = -3.462-4·1·1
Δ = 7.9716
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{-(-3.46)-\sqrt{7.9716}}{2*1}=\frac{3.46-\sqrt{7.9716}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.46)+\sqrt{7.9716}}{2*1}=\frac{3.46+\sqrt{7.9716}}{2}
$