12=1/3x+8,x=

Solution for 12=1/3x+8,x= equation:

12=1/3x+8.x=

We move all terms to the left:

12-(1/3x+8.x)=0


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

x∈R


We add all the numbers together, and all the variables

-(+8.x+1/3x)+12=0

We get rid of parentheses

-8.x-1/3x+12=0

We multiply all the terms by the denominator


-(8.x)*3x+12*3x-1=0

We add all the numbers together, and all the variables

-(+8.x)*3x+12*3x-1=0

We multiply parentheses

-24x^2+12*3x-1=0

Wy multiply elements

-24x^2+36x-1=0

a = -24; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-24)·(-1)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20\sqrt{3}}{2*-24}=\frac{-36-20\sqrt{3}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20\sqrt{3}}{2*-24}=\frac{-36+20\sqrt{3}}{-48}
$