3x-(1/2x)=189

Solution for 3x-(1/2x)=189 equation:

3x-(1/2x)=189

We move all terms to the left:

3x-(1/2x)-(189)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+1/2x)-189=0

We get rid of parentheses

3x-1/2x-189=0

We multiply all the terms by the denominator


3x*2x-189*2x-1=0

Wy multiply elements

6x^2-378x-1=0

a = 6; b = -378; c = -1;
Δ = b2-4ac
Δ = -3782-4·6·(-1)
Δ = 142908
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:

$\sqrt{\Delta}=\sqrt{142908}=\sqrt{4*35727}=\sqrt{4}*\sqrt{35727}=2\sqrt{35727}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-2\sqrt{35727}}{2*6}=\frac{378-2\sqrt{35727}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+2\sqrt{35727}}{2*6}=\frac{378+2\sqrt{35727}}{12}
$