2*x+2/x=45

Solution for 2*x+2/x=45 equation:

2x+2/x=45

We move all terms to the left:

2x+2/x-(45)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-45*x+2=0

We add all the numbers together, and all the variables

-45x+2x*x+2=0

Wy multiply elements

2x^2-45x+2=0

a = 2; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·2·2
Δ = 2009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-7\sqrt{41}}{2*2}=\frac{45-7\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+7\sqrt{41}}{2*2}=\frac{45+7\sqrt{41}}{4}
$