(2/x+4)+(5/5x+20)=5

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Solution for (2/x+4)+(5/5x+20)=5 equation: 



(2/x+4)+(5/5x+20)=5

We move all terms to the left:

(2/x+4)+(5/5x+20)-(5)=0



Domain of the equation: x+4)!=0

x∈R





Domain of the equation: 5x+20)!=0

x∈R



We get rid of parentheses

2/x+5/5x+4+20-5=0

We calculate fractions


10x/5x^2+5x/5x^2+4+20-5=0

We add all the numbers together, and all the variables

10x/5x^2+5x/5x^2+19=0

We multiply all the terms by the denominator


10x+5x+19*5x^2=0

We add all the numbers together, and all the variables

15x+19*5x^2=0

Wy multiply elements

95x^2+15x=0

a = 95; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·95·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*95}=\frac{-30}{190}
=-3/19
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*95}=\frac{0}{190}
=0
$

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