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

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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 $

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