-3x=1/3x+9

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

-3x=1/3x+9

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

-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 = 693
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:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{77}}{2*-9}=\frac{27-3\sqrt{77}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{77}}{2*-9}=\frac{27+3\sqrt{77}}{-18}
$