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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


25x/20x^2+(-16x)/20x^2-1-1=0

We add all the numbers together, and all the variables

25x/20x^2+(-16x)/20x^2-2=0

We multiply all the terms by the denominator


25x+(-16x)-2*20x^2=0

Wy multiply elements

-40x^2+25x+(-16x)=0

We get rid of parentheses

-40x^2+25x-16x=0

We add all the numbers together, and all the variables

-40x^2+9x=0

a = -40; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-40)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-40}=\frac{-18}{-80}
=9/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-40}=\frac{0}{-80}
=0
$