4/2x=5/3x+2

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



4/2x=5/3x+2
We move all terms to the left:
4/2x-(5/3x+2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x+2)!=0
x∈R
We get rid of parentheses
4/2x-5/3x-2=0
We calculate fractions
12x/6x^2+(-10x)/6x^2-2=0
We multiply all the terms by the denominator
12x+(-10x)-2*6x^2=0
Wy multiply elements
-12x^2+12x+(-10x)=0
We get rid of parentheses
-12x^2+12x-10x=0
We add all the numbers together, and all the variables
-12x^2+2x=0
a = -12; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-12)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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

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