1/2x+2/3=1/4,x

Solution for 1/2x+2/3=1/4,x equation:

1/2x+2/3=1/4.x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/2x-1/4.x+2/3=0

We calculate fractions


64x^2/24x^2+12x/24x^2+(-18x)/24x^2=0

We multiply all the terms by the denominator


64x^2+12x+(-18x)=0

We get rid of parentheses

64x^2+12x-18x=0

We add all the numbers together, and all the variables

64x^2-6x=0

a = 64; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·64·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*64}=\frac{12}{128}
=3/32
$