3x-(1/2x)=60

Solution for 3x-(1/2x)=60 equation:

3x-(1/2x)=60

We move all terms to the left:

3x-(1/2x)-(60)=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)-60=0

We get rid of parentheses

3x-1/2x-60=0

We multiply all the terms by the denominator


3x*2x-60*2x-1=0

Wy multiply elements

6x^2-120x-1=0

a = 6; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·6·(-1)
Δ = 14424
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:

$\sqrt{\Delta}=\sqrt{14424}=\sqrt{4*3606}=\sqrt{4}*\sqrt{3606}=2\sqrt{3606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3606}}{2*6}=\frac{120-2\sqrt{3606}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3606}}{2*6}=\frac{120+2\sqrt{3606}}{12}
$