1/3x-3x=-9

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

1/3x-3x=-9

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+27x+1=0

a = -9; b = 27; c = +1;
Δ = b2-4ac
Δ = 272-4·(-9)·1
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{85}}{2*-9}=\frac{-27-3\sqrt{85}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{85}}{2*-9}=\frac{-27+3\sqrt{85}}{-18}
$