2x+2/x-4=0.5

Solution for 2x+2/x-4=0.5 equation:

2x+2/x-4=0.5

We move all terms to the left:

2x+2/x-4-(0.5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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}
$