3/4x-2/3=1/3x-5

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Solution for 3/4x-2/3=1/3x-5 equation:



3/4x-2/3=1/3x-5
We move all terms to the left:
3/4x-2/3-(1/3x-5)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x-5)!=0
x∈R
We get rid of parentheses
3/4x-1/3x+5-2/3=0
We calculate fractions
81x/108x^2+(-4x)/108x^2+(-8x)/108x^2+5=0
We multiply all the terms by the denominator
81x+(-4x)+(-8x)+5*108x^2=0
Wy multiply elements
540x^2+81x+(-4x)+(-8x)=0
We get rid of parentheses
540x^2+81x-4x-8x=0
We add all the numbers together, and all the variables
540x^2+69x=0
a = 540; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·540·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*540}=\frac{-138}{1080} =-23/180 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*540}=\frac{0}{1080} =0 $

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