9/10x=10/11x-1

Solution for 9/10x=10/11x-1 equation:

9/10x=10/11x-1

We move all terms to the left:

9/10x-(10/11x-1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 11x-1)!=0

x∈R


We get rid of parentheses

9/10x-10/11x+1=0

We calculate fractions


99x/110x^2+(-100x)/110x^2+1=0

We multiply all the terms by the denominator


99x+(-100x)+1*110x^2=0

Wy multiply elements

110x^2+99x+(-100x)=0

We get rid of parentheses

110x^2+99x-100x=0

We add all the numbers together, and all the variables

110x^2-1x=0

a = 110; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·110·0
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*110}=\frac{0}{220}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*110}=\frac{2}{220}
=1/110
$