1/2x-2/5=8/10x

Solution for 1/2x-2/5=8/10x equation:

1/2x-2/5=8/10x

We move all terms to the left:

1/2x-2/5-(8/10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+8/10x)-2/5=0

We get rid of parentheses

1/2x-8/10x-2/5=0

We calculate fractions


(-40x^2)/500x^2+250x/500x^2+(-400x)/500x^2=0

We multiply all the terms by the denominator


(-40x^2)+250x+(-400x)=0

We get rid of parentheses

-40x^2+250x-400x=0

We add all the numbers together, and all the variables

-40x^2-150x=0

a = -40; b = -150; c = 0;
Δ = b2-4ac
Δ = -1502-4·(-40)·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150}{2*-40}=\frac{300}{-80}
=-3+3/4
$