3/11x=9,x

Solution for 3/11x=9,x equation:

3/11x=9.x

We move all terms to the left:

3/11x-(9.x)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We add all the numbers together, and all the variables

3/11x-(+9.x)=0

We get rid of parentheses

3/11x-9.x=0

We multiply all the terms by the denominator


-(9.x)*11x+3=0

We add all the numbers together, and all the variables

-(+9.x)*11x+3=0

We multiply parentheses

-99x^2+3=0

a = -99; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-99)·3
Δ = 1188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{33}}{2*-99}=\frac{0-6\sqrt{33}}{-198}
=-\frac{6\sqrt{33}}{-198}
=-\frac{\sqrt{33}}{-33}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{33}}{2*-99}=\frac{0+6\sqrt{33}}{-198}
=\frac{6\sqrt{33}}{-198}
=\frac{\sqrt{33}}{-33}
$