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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

1/5x-5/4x-1-4=0

We calculate fractions


4x/20x^2+(-25x)/20x^2-1-4=0

We add all the numbers together, and all the variables

4x/20x^2+(-25x)/20x^2-5=0

We multiply all the terms by the denominator


4x+(-25x)-5*20x^2=0

Wy multiply elements

-100x^2+4x+(-25x)=0

We get rid of parentheses

-100x^2+4x-25x=0

We add all the numbers together, and all the variables

-100x^2-21x=0

a = -100; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-100)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-100}=\frac{42}{-200}
=-21/100
$