-.5=3x-1/3x

Solution for -.5=3x-1/3x equation:

-.5=3x-1/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3x-1/3x)-.5=0

We add all the numbers together, and all the variables

-(+3x-1/3x)-0.5=0

We get rid of parentheses

-3x+1/3x-0.5=0

We multiply all the terms by the denominator


-3x*3x-(0.5)*3x+1=0

We multiply parentheses

-3x*3x-1.5x+1=0

Wy multiply elements

-9x^2-1.5x+1=0

a = -9; b = -1.5; c = +1;
Δ = b2-4ac
Δ = -1.52-4·(-9)·1
Δ = 38.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{38.25}}{2*-9}=\frac{1.5-\sqrt{38.25}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{38.25}}{2*-9}=\frac{1.5+\sqrt{38.25}}{-18}
$