x+(1/3x+8)=-36

Solution for x+(1/3x+8)=-36 equation:

x+(1/3x+8)=-36

We move all terms to the left:

x+(1/3x+8)-(-36)=0


Domain of the equation: 3x+8)!=0

x∈R


We add all the numbers together, and all the variables

x+(1/3x+8)+36=0

We get rid of parentheses

x+1/3x+8+36=0

We multiply all the terms by the denominator


x*3x+8*3x+36*3x+1=0

Wy multiply elements

3x^2+24x+108x+1=0

We add all the numbers together, and all the variables

3x^2+132x+1=0

a = 3; b = 132; c = +1;
Δ = b2-4ac
Δ = 1322-4·3·1
Δ = 17412
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:

$\sqrt{\Delta}=\sqrt{17412}=\sqrt{4*4353}=\sqrt{4}*\sqrt{4353}=2\sqrt{4353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-2\sqrt{4353}}{2*3}=\frac{-132-2\sqrt{4353}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+2\sqrt{4353}}{2*3}=\frac{-132+2\sqrt{4353}}{6}
$