20x/4x-1+2/x=5

Solution for 20x/4x-1+2/x=5 equation:

20x/4x-1+2/x=5

We move all terms to the left:

20x/4x-1+2/x-(5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

20x/4x+2/x-6=0

We calculate fractions


20x^2/4x^2+8x/4x^2-6=0

We multiply all the terms by the denominator


20x^2+8x-6*4x^2=0

Wy multiply elements

20x^2-24x^2+8x=0

We add all the numbers together, and all the variables

-4x^2+8x=0

a = -4; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-4)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-4}=\frac{0}{-8}
=0
$