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

Solution for 5x/(2x-1)-4x=0 equation:

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


Domain of the equation: (2x-1)!=0

We move all terms containing x to the left, all other terms to the right

2x!=1

x!=1/2

x!=1/2

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x-4x*(2x-1)=0

We multiply parentheses

-8x^2+5x+4x=0

We add all the numbers together, and all the variables

-8x^2+9x=0

a = -8; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-8)·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*-8}=\frac{-18}{-16}
=1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-8}=\frac{0}{-16}
=0
$