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

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



3/x-4=5/2x-3
We move all terms to the left:
3/x-4-(5/2x-3)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x-3)!=0
x∈R
We get rid of parentheses
3/x-5/2x+3-4=0
We calculate fractions
6x/2x^2+(-5x)/2x^2+3-4=0
We add all the numbers together, and all the variables
6x/2x^2+(-5x)/2x^2-1=0
We multiply all the terms by the denominator
6x+(-5x)-1*2x^2=0
Wy multiply elements
-2x^2+6x+(-5x)=0
We get rid of parentheses
-2x^2+6x-5x=0
We add all the numbers together, and all the variables
-2x^2+x=0
a = -2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-2}=\frac{-2}{-4} =1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-2}=\frac{0}{-4} =0 $

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