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

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



4/x-3=5/2x+3
We move all terms to the left:
4/x-3-(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
4/x-5/2x-3-3=0
We calculate fractions
8x/2x^2+(-5x)/2x^2-3-3=0
We add all the numbers together, and all the variables
8x/2x^2+(-5x)/2x^2-6=0
We multiply all the terms by the denominator
8x+(-5x)-6*2x^2=0
Wy multiply elements
-12x^2+8x+(-5x)=0
We get rid of parentheses
-12x^2+8x-5x=0
We add all the numbers together, and all the variables
-12x^2+3x=0
a = -12; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-12)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-12}=\frac{-6}{-24} =1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-12}=\frac{0}{-24} =0 $

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