3x-5=-(1/2x)

Solution for 3x-5=-(1/2x) equation:

3x-5=-(1/2x)

We move all terms to the left:

3x-5-(-(1/2x))=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))-5=0

We multiply all the terms by the denominator


3x*2x))-(-(-5*2x))+1=0

Wy multiply elements

6x^2-10x=0

a = 6; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·6·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*6}=\frac{20}{12}
=1+2/3
$