3x+5=-1/3x-1

Solution for 3x+5=-1/3x-1 equation:

3x+5=-1/3x-1

We move all terms to the left:

3x+5-(-1/3x-1)=0


Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

3x+1/3x+1+5=0

We multiply all the terms by the denominator


3x*3x+1*3x+5*3x+1=0

Wy multiply elements

9x^2+3x+15x+1=0

We add all the numbers together, and all the variables

9x^2+18x+1=0

a = 9; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·9·1
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{2}}{2*9}=\frac{-18-12\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{2}}{2*9}=\frac{-18+12\sqrt{2}}{18}
$