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

131x+(-3x)+3*192x^2=0

Wy multiply elements

576x^2+131x+(-3x)=0

We get rid of parentheses

576x^2+131x-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{-256}{1152}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*576}=\frac{0}{1152}
=0
$