3x-66=x-28+1/3x=14

Solution for 3x-66=x-28+1/3x=14 equation:

3x-66=x-28+1/3x=14

We move all terms to the left:

3x-66-(x-28+1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(x+1/3x-28)-66=0

We get rid of parentheses

3x-x-1/3x+28-66=0

We multiply all the terms by the denominator


3x*3x-x*3x+28*3x-66*3x-1=0

Wy multiply elements

9x^2-3x^2+84x-198x-1=0

We add all the numbers together, and all the variables

6x^2-114x-1=0

a = 6; b = -114; c = -1;
Δ = b2-4ac
Δ = -1142-4·6·(-1)
Δ = 13020
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:

$\sqrt{\Delta}=\sqrt{13020}=\sqrt{4*3255}=\sqrt{4}*\sqrt{3255}=2\sqrt{3255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3255}}{2*6}=\frac{114-2\sqrt{3255}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3255}}{2*6}=\frac{114+2\sqrt{3255}}{12}
$