2x+2x+(5/2x)=17

Solution for 2x+2x+(5/2x)=17 equation:

2x+2x+(5/2x)=17

We move all terms to the left:

2x+2x+(5/2x)-(17)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2x+(+5/2x)-17=0

We add all the numbers together, and all the variables

4x+(+5/2x)-17=0

We get rid of parentheses

4x+5/2x-17=0

We multiply all the terms by the denominator


4x*2x-17*2x+5=0

Wy multiply elements

8x^2-34x+5=0

a = 8; b = -34; c = +5;
Δ = b2-4ac
Δ = -342-4·8·5
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{249}}{2*8}=\frac{34-2\sqrt{249}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{249}}{2*8}=\frac{34+2\sqrt{249}}{16}
$