X/10x=2/5x

Solution for X/10x=2/5x equation:

X/10X=2/5X

We move all terms to the left:

X/10X-(2/5X)=0


Domain of the equation: 10X!=0

X!=0/10

X!=0

X∈R



Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X/10X-(+2/5X)=0

We get rid of parentheses

X/10X-2/5X=0

We calculate fractions


5X^2/50X^2+(-20X)/50X^2=0

We multiply all the terms by the denominator


5X^2+(-20X)=0

We get rid of parentheses

5X^2-20X=0

a = 5; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·5·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*5}=\frac{0}{10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*5}=\frac{40}{10}
=4
$