1/5x-2=x-1

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

1/5x-2=x-1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2+5x-10x+1=0

We add all the numbers together, and all the variables

-5x^2-5x+1=0

a = -5; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-5)·1
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*-5}=\frac{5-3\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*-5}=\frac{5+3\sqrt{5}}{-10}
$