x-2=4.83/x

Solution for x-2=4.83/x equation:

x-2=4.83/x

We move all terms to the left:

x-2-(4.83/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-(+4.83/x)-2=0

We get rid of parentheses

x-4.83/x-2=0

We multiply all the terms by the denominator


x*x-2*x-4.83=0

We add all the numbers together, and all the variables

-2x+x*x-4.83=0

Wy multiply elements

x^2-2x-4.83=0

a = 1; b = -2; c = -4.83;
Δ = b2-4ac
Δ = -22-4·1·(-4.83)
Δ = 23.32
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{-(-2)-\sqrt{23.32}}{2*1}=\frac{2-\sqrt{23.32}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{23.32}}{2*1}=\frac{2+\sqrt{23.32}}{2}
$