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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2+27x+3x+1=0

We add all the numbers together, and all the variables

9x^2+30x+1=0

a = 9; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·9·1
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{6}}{2*9}=\frac{-30-12\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{6}}{2*9}=\frac{-30+12\sqrt{6}}{18}
$