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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


16x^2/72x^2+18x/72x^2+(-36x)/72x^2-2=0

We multiply all the terms by the denominator


16x^2+18x+(-36x)-2*72x^2=0

Wy multiply elements

16x^2-144x^2+18x+(-36x)=0

We get rid of parentheses

16x^2-144x^2+18x-36x=0

We add all the numbers together, and all the variables

-128x^2-18x=0

a = -128; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-128)·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*-128}=\frac{0}{-256}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-128}=\frac{36}{-256}
=-9/64
$