1/4(2x-1)=1/3(2-x)

Solution for 1/4(2x-1)=1/3(2-x) equation:

1/4(2x-1)=1/3(2-x)

We move all terms to the left:

1/4(2x-1)-(1/3(2-x))=0


Domain of the equation: 4(2x-1)!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

1/4(2x-1)-(1/3(-1x+2))=0

We calculate fractions


(3x(-)/(4(2x-1)*3(-1x+2)))+(-4x2/(4(2x-1)*3(-1x+2)))=0


We calculate terms in parentheses: +(3x(-)/(4(2x-1)*3(-1x+2))), so:

3x(-)/(4(2x-1)*3(-1x+2))

We add all the numbers together, and all the variables

3x0/(4(2x-1)*3(-1x+2))

We multiply all the terms by the denominator


3x0

We add all the numbers together, and all the variables

3x

Back to the equation:

+(3x)



We calculate terms in parentheses: +(-4x2/(4(2x-1)*3(-1x+2))), so:

-4x2/(4(2x-1)*3(-1x+2))

We multiply all the terms by the denominator


-4x2

We add all the numbers together, and all the variables

-4x^2

Back to the equation:

+(-4x^2)


We get rid of parentheses

-4x^2+3x=0

a = -4; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-4}=\frac{-6}{-8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-4}=\frac{0}{-8}
=0
$