4.5=2x+2/x

Solution for 4.5=2x+2/x equation:

4.5=2x+2/x

We move all terms to the left:

4.5-(2x+2/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

-(+2x+2/x)+4.5=0

We get rid of parentheses

-2x-2/x+4.5=0

We multiply all the terms by the denominator


-2x*x+(4.5)*x-2=0

We multiply parentheses

-2x*x+4.5x-2=0

Wy multiply elements

-2x^2+4.5x-2=0

a = -2; b = 4.5; c = -2;
Δ = b2-4ac
Δ = 4.52-4·(-2)·(-2)
Δ = 4.25
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{-(4.5)-\sqrt{4.25}}{2*-2}=\frac{-4.5-\sqrt{4.25}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{4.25}}{2*-2}=\frac{-4.5+\sqrt{4.25}}{-4}
$