2/5x-5/2x=1/10

Solution for 2/5x-5/2x=1/10 equation:

2/5x-5/2x=1/10

We move all terms to the left:

2/5x-5/2x-(1/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-5/2x-(+1/10)=0

We get rid of parentheses

2/5x-5/2x-1/10=0

We calculate fractions


(-20x^2)/100x^2+40x/100x^2+(-250x)/100x^2=0

We multiply all the terms by the denominator


(-20x^2)+40x+(-250x)=0

We get rid of parentheses

-20x^2+40x-250x=0

We add all the numbers together, and all the variables

-20x^2-210x=0

a = -20; b = -210; c = 0;
Δ = b2-4ac
Δ = -2102-4·(-20)·0
Δ = 44100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44100}=210$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-210}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+210}{2*-20}=\frac{420}{-40}
=-10+1/2
$