7/3x+5=5/6x-3

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Solution for 7/3x+5=5/6x-3 equation:



7/3x+5=5/6x-3
We move all terms to the left:
7/3x+5-(5/6x-3)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x-3)!=0
x∈R
We get rid of parentheses
7/3x-5/6x+3+5=0
We calculate fractions
42x/18x^2+(-15x)/18x^2+3+5=0
We add all the numbers together, and all the variables
42x/18x^2+(-15x)/18x^2+8=0
We multiply all the terms by the denominator
42x+(-15x)+8*18x^2=0
Wy multiply elements
144x^2+42x+(-15x)=0
We get rid of parentheses
144x^2+42x-15x=0
We add all the numbers together, and all the variables
144x^2+27x=0
a = 144; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·144·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*144}=\frac{-54}{288} =-3/16 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*144}=\frac{0}{288} =0 $

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