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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


5x/20x^2+(-12x)/20x^2-4-1=0

We add all the numbers together, and all the variables

5x/20x^2+(-12x)/20x^2-5=0

We multiply all the terms by the denominator


5x+(-12x)-5*20x^2=0

Wy multiply elements

-100x^2+5x+(-12x)=0

We get rid of parentheses

-100x^2+5x-12x=0

We add all the numbers together, and all the variables

-100x^2-7x=0

a = -100; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-100)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-100}=\frac{14}{-200}
=-7/100
$