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

Solution for 4/x-4-2/5x-20=0 equation:

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

4/x-2/5x-24=0

We calculate fractions


20x/5x^2+(-2x)/5x^2-24=0

We multiply all the terms by the denominator


20x+(-2x)-24*5x^2=0

Wy multiply elements

-120x^2+20x+(-2x)=0

We get rid of parentheses

-120x^2+20x-2x=0

We add all the numbers together, and all the variables

-120x^2+18x=0

a = -120; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-120)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-120}=\frac{-36}{-240}
=3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-120}=\frac{0}{-240}
=0
$