10/x=7/6x+1

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Solution for 10/x=7/6x+1 equation:



10/x=7/6x+1
We move all terms to the left:
10/x-(7/6x+1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 6x+1)!=0
x∈R
We get rid of parentheses
10/x-7/6x-1=0
We calculate fractions
60x/6x^2+(-7x)/6x^2-1=0
We multiply all the terms by the denominator
60x+(-7x)-1*6x^2=0
Wy multiply elements
-6x^2+60x+(-7x)=0
We get rid of parentheses
-6x^2+60x-7x=0
We add all the numbers together, and all the variables
-6x^2+53x=0
a = -6; b = 53; c = 0;
Δ = b2-4ac
Δ = 532-4·(-6)·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-53}{2*-6}=\frac{-106}{-12} =8+5/6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+53}{2*-6}=\frac{0}{-12} =0 $

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