x=2x-4/5x-1

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

x=2x-4/5x-1

We move all terms to the left:

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


Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-10x^2+5x+4=0

We add all the numbers together, and all the variables

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

a = -5; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-5)·4
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{105}}{2*-5}=\frac{-5-\sqrt{105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{105}}{2*-5}=\frac{-5+\sqrt{105}}{-10}
$