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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


32x^2/72x^2+18x/72x^2+(-36x)/72x^2-1=0

We multiply all the terms by the denominator


32x^2+18x+(-36x)-1*72x^2=0

Wy multiply elements

32x^2-72x^2+18x+(-36x)=0

We get rid of parentheses

32x^2-72x^2+18x-36x=0

We add all the numbers together, and all the variables

-40x^2-18x=0

a = -40; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-40)·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*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-40}=\frac{36}{-80}
=-9/20
$