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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-128x)/192x^2+(-3x)/192x^2+3x/192x^2-3=0

We multiply all the terms by the denominator


(-128x)+(-3x)+3x-3*192x^2=0

We add all the numbers together, and all the variables

3x+(-128x)+(-3x)-3*192x^2=0

Wy multiply elements

-576x^2+3x+(-128x)+(-3x)=0

We get rid of parentheses

-576x^2+3x-128x-3x=0

We add all the numbers together, and all the variables

-576x^2-128x=0

a = -576; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·(-576)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*-576}=\frac{0}{-1152}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*-576}=\frac{256}{-1152}
=-2/9
$