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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


(-50x^2)/100x^2+()/100x^2+(-(1*5x*2)/100x^2=0

We add all the numbers together, and all the variables

(-50x^2)/100x^2+()/100x^2+(-(+1*5x*2)/100x^2=0

We multiply all the terms by the denominator


(-50x^2)+(-(+1*5x*2)+()=0


We calculate terms in parentheses: +(-(+1*5x*2)+(), so:

-(+1*5x*2)+(

We add all the numbers together, and all the variables

-(+1*5x*2)

We get rid of parentheses

-1*5x*2

Wy multiply elements

-10x*2

Wy multiply elements

-20x

Back to the equation:

+(-20x)


We get rid of parentheses

-50x^2-20x=0

a = -50; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-50)·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*-50}=\frac{0}{-100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-50}=\frac{40}{-100}
=-2/5
$