1/3x+(2x+8)+x=205

Solution for 1/3x+(2x+8)+x=205 equation:

1/3x+(2x+8)+x=205

We move all terms to the left:

1/3x+(2x+8)+x-(205)=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+1/3x+(2x+8)-205=0

We get rid of parentheses

x+1/3x+2x+8-205=0

We multiply all the terms by the denominator


x*3x+2x*3x+8*3x-205*3x+1=0

Wy multiply elements

3x^2+6x^2+24x-615x+1=0

We add all the numbers together, and all the variables

9x^2-591x+1=0

a = 9; b = -591; c = +1;
Δ = b2-4ac
Δ = -5912-4·9·1
Δ = 349245
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:

$\sqrt{\Delta}=\sqrt{349245}=\sqrt{9*38805}=\sqrt{9}*\sqrt{38805}=3\sqrt{38805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-591)-3\sqrt{38805}}{2*9}=\frac{591-3\sqrt{38805}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-591)+3\sqrt{38805}}{2*9}=\frac{591+3\sqrt{38805}}{18}
$