1/5-1/2*x=9/10*x

Solution for 1/5-1/2*x=9/10*x equation:

1/5-1/2x=9/10x

We move all terms to the left:

1/5-1/2x-(9/10x)=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-(+9/10x)+1/5=0

We get rid of parentheses

-1/2x-9/10x+1/5=0

We calculate fractions


20x^2/500x^2+(-250x)/500x^2+(-450x)/500x^2=0

We multiply all the terms by the denominator


20x^2+(-250x)+(-450x)=0

We get rid of parentheses

20x^2-250x-450x=0

We add all the numbers together, and all the variables

20x^2-700x=0

a = 20; b = -700; c = 0;
Δ = b2-4ac
Δ = -7002-4·20·0
Δ = 490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{490000}=700$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-700}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+700}{2*20}=\frac{1400}{40}
=35
$