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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

1/5x-1/4x-2-1=0

We calculate fractions


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

We add all the numbers together, and all the variables

4x/20x^2+(-5x)/20x^2-3=0

We multiply all the terms by the denominator


4x+(-5x)-3*20x^2=0

Wy multiply elements

-60x^2+4x+(-5x)=0

We get rid of parentheses

-60x^2+4x-5x=0

We add all the numbers together, and all the variables

-60x^2-1x=0

a = -60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-60}=\frac{2}{-120}
=-1/60
$