1/5x-4=3/4x+1

Solution for 1/5x-4=3/4x+1 equation:

1/5x-4=3/4x+1

We move all terms to the left:

1/5x-4-(3/4x+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-3/4x-1-4=0

We calculate fractions


4x/20x^2+(-15x)/20x^2-1-4=0

We add all the numbers together, and all the variables

4x/20x^2+(-15x)/20x^2-5=0

We multiply all the terms by the denominator


4x+(-15x)-5*20x^2=0

Wy multiply elements

-100x^2+4x+(-15x)=0

We get rid of parentheses

-100x^2+4x-15x=0

We add all the numbers together, and all the variables

-100x^2-11x=0

a = -100; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-100)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-100}=\frac{22}{-200}
=-11/100
$