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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

(x+8)+1/3x-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^2-84x+1=0

a = 3; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·3·1
Δ = 7044
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:

$\sqrt{\Delta}=\sqrt{7044}=\sqrt{4*1761}=\sqrt{4}*\sqrt{1761}=2\sqrt{1761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1761}}{2*3}=\frac{84-2\sqrt{1761}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1761}}{2*3}=\frac{84+2\sqrt{1761}}{6}
$