1/5x=1/4x-5

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

1/5x=1/4x-5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

100x^2+4x+(-5x)=0

We get rid of parentheses

100x^2+4x-5x=0

We add all the numbers together, and all the variables

100x^2-1x=0

a = 100; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·100·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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