2x+3*1/2x=105

Solution for 2x+3*1/2x=105 equation:

2x+3*1/2x=105

We move all terms to the left:

2x+3*1/2x-(105)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-105*2x+3*1=0

We add all the numbers together, and all the variables

2x*2x-105*2x+3=0

Wy multiply elements

4x^2-210x+3=0

a = 4; b = -210; c = +3;
Δ = b2-4ac
Δ = -2102-4·4·3
Δ = 44052
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:

$\sqrt{\Delta}=\sqrt{44052}=\sqrt{4*11013}=\sqrt{4}*\sqrt{11013}=2\sqrt{11013}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11013}}{2*4}=\frac{210-2\sqrt{11013}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11013}}{2*4}=\frac{210+2\sqrt{11013}}{8}
$