1/3x+0.5=2x

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Solution for 1/3x+0.5=2x equation: 



1/3x+0.5=2x

We move all terms to the left:

1/3x+0.5-(2x)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

-2x+1/3x+0.5=0

We multiply all the terms by the denominator


-2x*3x+(0.5)*3x+1=0

We multiply parentheses

-2x*3x+1.5x+1=0

Wy multiply elements

-6x^2+1.5x+1=0

a = -6; b = 1.5; c = +1;
Δ = b2-4ac
Δ = 1.52-4·(-6)·1
Δ = 26.25
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{26.25}}{2*-6}=\frac{-1.5-\sqrt{26.25}}{-12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{26.25}}{2*-6}=\frac{-1.5+\sqrt{26.25}}{-12}
$

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