1/3(2x-1)-(2x+1)=1/12(2-x)

Solution for 1/3(2x-1)-(2x+1)=1/12(2-x) equation:

1/3(2x-1)-(2x+1)=1/12(2-x)

We move all terms to the left:

1/3(2x-1)-(2x+1)-(1/12(2-x))=0


Domain of the equation: 3(2x-1)!=0

x∈R



Domain of the equation: 12(2-x))!=0

x∈R


We add all the numbers together, and all the variables

1/3(2x-1)-(2x+1)-(1/12(-1x+2))=0

We get rid of parentheses

1/3(2x-1)-2x-(1/12(-1x+2))-1=0

We calculate fractions


-2x+(12x(-)/(3(2x-1)*12(-1x+2)))+(-3x2/(3(2x-1)*12(-1x+2)))-1=0


We calculate terms in parentheses: +(12x(-)/(3(2x-1)*12(-1x+2))), so:

12x(-)/(3(2x-1)*12(-1x+2))

We add all the numbers together, and all the variables

12x0/(3(2x-1)*12(-1x+2))

We multiply all the terms by the denominator


12x0

We add all the numbers together, and all the variables

12x

Back to the equation:

+(12x)



We calculate terms in parentheses: +(-3x2/(3(2x-1)*12(-1x+2))), so:

-3x2/(3(2x-1)*12(-1x+2))

We multiply all the terms by the denominator


-3x2

We add all the numbers together, and all the variables

-3x^2

Back to the equation:

+(-3x^2)


We add all the numbers together, and all the variables

(-3x^2)+10x-1=0

We get rid of parentheses

-3x^2+10x-1=0

a = -3; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-3)·(-1)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{22}}{2*-3}=\frac{-10-2\sqrt{22}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{22}}{2*-3}=\frac{-10+2\sqrt{22}}{-6}
$