9=1/3x+9x=1

Solution for 9=1/3x+9x=1 equation:

9=1/3x+9x=1

We move all terms to the left:

9-(1/3x+9x)=0


Domain of the equation: 3x+9x)!=0

x∈R


We add all the numbers together, and all the variables

-(+9x+1/3x)+9=0

We get rid of parentheses

-9x-1/3x+9=0

We multiply all the terms by the denominator


-9x*3x+9*3x-1=0

Wy multiply elements

-27x^2+27x-1=0

a = -27; b = 27; c = -1;
Δ = b2-4ac
Δ = 272-4·(-27)·(-1)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{69}}{2*-27}=\frac{-27-3\sqrt{69}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{69}}{2*-27}=\frac{-27+3\sqrt{69}}{-54}
$