5/x-7=6x

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



5/x-7=6x
We move all terms to the left:
5/x-7-(6x)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
-6x+5/x-7=0
We multiply all the terms by the denominator
-6x*x-7*x+5=0
We add all the numbers together, and all the variables
-7x-6x*x+5=0
Wy multiply elements
-6x^2-7x+5=0
a = -6; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-6)·5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-6}=\frac{-6}{-12} =1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-6}=\frac{20}{-12} =-1+2/3 $

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