2-3/7x=-2/3x

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Solution for 2-3/7x=-2/3x equation:



2-3/7x=-2/3x
We move all terms to the left:
2-3/7x-(-2/3x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We get rid of parentheses
-3/7x+2/3x+2=0
We calculate fractions
(-9x)/21x^2+14x/21x^2+2=0
We multiply all the terms by the denominator
(-9x)+14x+2*21x^2=0
We add all the numbers together, and all the variables
14x+(-9x)+2*21x^2=0
Wy multiply elements
42x^2+14x+(-9x)=0
We get rid of parentheses
42x^2+14x-9x=0
We add all the numbers together, and all the variables
42x^2+5x=0
a = 42; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·42·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*42}=\frac{-10}{84} =-5/42 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*42}=\frac{0}{84} =0 $

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