X-2=1/5x

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

X-2=1/5X

We move all terms to the left:

X-2-(1/5X)=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-(+1/5X)-2=0

We get rid of parentheses

X-1/5X-2=0

We multiply all the terms by the denominator


X*5X-2*5X-1=0

Wy multiply elements

5X^2-10X-1=0

a = 5; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·5·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{30}}{2*5}=\frac{10-2\sqrt{30}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{30}}{2*5}=\frac{10+2\sqrt{30}}{10}
$