6/x+6/5x=1

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Solution for 6/x+6/5x=1 equation:



6/x+6/5x=1
We move all terms to the left:
6/x+6/5x-(1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We calculate fractions
30x/5x^2+6x/5x^2-1=0
We multiply all the terms by the denominator
30x+6x-1*5x^2=0
We add all the numbers together, and all the variables
36x-1*5x^2=0
Wy multiply elements
-5x^2+36x=0
a = -5; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-5)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-5}=\frac{-72}{-10} =7+1/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-5}=\frac{0}{-10} =0 $

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