5/6x-1=1/3x+7

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Solution for 5/6x-1=1/3x+7 equation:



5/6x-1=1/3x+7
We move all terms to the left:
5/6x-1-(1/3x+7)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 3x+7)!=0
x∈R
We get rid of parentheses
5/6x-1/3x-7-1=0
We calculate fractions
15x/18x^2+(-6x)/18x^2-7-1=0
We add all the numbers together, and all the variables
15x/18x^2+(-6x)/18x^2-8=0
We multiply all the terms by the denominator
15x+(-6x)-8*18x^2=0
Wy multiply elements
-144x^2+15x+(-6x)=0
We get rid of parentheses
-144x^2+15x-6x=0
We add all the numbers together, and all the variables
-144x^2+9x=0
a = -144; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-144)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-144}=\frac{-18}{-288} =1/16 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-144}=\frac{0}{-288} =0 $

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