2/x+5+1/5x+25=16

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Solution for 2/x+5+1/5x+25=16 equation: 



2/x+5+1/5x+25=16

We move all terms to the left:

2/x+5+1/5x+25-(16)=0



Domain of the equation: x!=0

x∈R





Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

2/x+1/5x+14=0

We calculate fractions


10x/5x^2+x/5x^2+14=0

We multiply all the terms by the denominator


10x+x+14*5x^2=0

We add all the numbers together, and all the variables

11x+14*5x^2=0

Wy multiply elements

70x^2+11x=0

a = 70; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·70·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*70}=\frac{-22}{140}
=-11/70
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*70}=\frac{0}{140}
=0
$

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