(1/3)x+(5/6)=2x

Solution for (1/3)x+(5/6)=2x equation:

(1/3)x+(5/6)=2x

We move all terms to the left:

(1/3)x+(5/6)-(2x)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)x-2x+(+5/6)=0

We add all the numbers together, and all the variables

-2x+(+1/3)x+(+5/6)=0

We multiply parentheses

x^2-2x+(+5/6)=0

We get rid of parentheses

x^2-2x+5/6=0

We multiply all the terms by the denominator


x^2*6-2x*6+5=0

Wy multiply elements

6x^2-12x+5=0

a = 6; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·6·5
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{6}}{2*6}=\frac{12-2\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*6}=\frac{12+2\sqrt{6}}{12}
$