x-1=4/5x

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

x-1=4/5x

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-4/5x-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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}
$