1/9x=20+1/10x

Solution for 1/9x=20+1/10x equation:

1/9x=20+1/10x

We move all terms to the left:

1/9x-(20+1/10x)=0


Domain of the equation: 9x!=0

x!=0/9

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

1/9x-(1/10x+20)=0

We get rid of parentheses

1/9x-1/10x-20=0

We calculate fractions


10x/90x^2+(-9x)/90x^2-20=0

We multiply all the terms by the denominator


10x+(-9x)-20*90x^2=0

Wy multiply elements

-1800x^2+10x+(-9x)=0

We get rid of parentheses

-1800x^2+10x-9x=0

We add all the numbers together, and all the variables

-1800x^2+x=0

a = -1800; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-1800)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-1800}=\frac{-2}{-3600}
=1/1800
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-1800}=\frac{0}{-3600}
=0
$