x/5x-4=4x

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

x/5x-4=4x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-4x*5x+x-4*5x=0

We add all the numbers together, and all the variables

x-4x*5x-4*5x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-20x^2-19x=0

a = -20; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-20)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-20}=\frac{38}{-40}
=-19/20
$