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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-64x^2)/72x^2+36x/72x^2+(-18x)/72x^2+1=0

We multiply all the terms by the denominator


(-64x^2)+36x+(-18x)+1*72x^2=0

Wy multiply elements

(-64x^2)+72x^2+36x+(-18x)=0

We get rid of parentheses

-64x^2+72x^2+36x-18x=0

We add all the numbers together, and all the variables

8x^2+18x=0

a = 8; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·8·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*8}=\frac{-36}{16}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*8}=\frac{0}{16}
=0
$