1/20x-1=9-1/5x

Solution for 1/20x-1=9-1/5x equation:

1/20x-1=9-1/5x

We move all terms to the left:

1/20x-1-(9-1/5x)=0


Domain of the equation: 20x!=0

x!=0/20

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

1/20x-(-1/5x+9)-1=0

We get rid of parentheses

1/20x+1/5x-9-1=0

We calculate fractions


5x/100x^2+20x/100x^2-9-1=0

We add all the numbers together, and all the variables

5x/100x^2+20x/100x^2-10=0

We multiply all the terms by the denominator


5x+20x-10*100x^2=0

We add all the numbers together, and all the variables

25x-10*100x^2=0

Wy multiply elements

-1000x^2+25x=0

a = -1000; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1000)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1000}=\frac{-50}{-2000}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1000}=\frac{0}{-2000}
=0
$