1/x+1/4x=20

Solution for 1/x+1/4x=20 equation:

1/x+1/4x=20

We move all terms to the left:

1/x+1/4x-(20)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


4x+x-20*4x^2=0

We add all the numbers together, and all the variables

5x-20*4x^2=0

Wy multiply elements

-80x^2+5x=0

a = -80; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-80)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-80}=\frac{-10}{-160}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-80}=\frac{0}{-160}
=0
$