1/3x+9=12+3x

Solution for 1/3x+9=12+3x equation:

1/3x+9=12+3x

We move all terms to the left:

1/3x+9-(12+3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(3x+12)+9=0

We get rid of parentheses

1/3x-3x-12+9=0

We multiply all the terms by the denominator


-3x*3x-12*3x+9*3x+1=0

Wy multiply elements

-9x^2-36x+27x+1=0

We add all the numbers together, and all the variables

-9x^2-9x+1=0

a = -9; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-9)·1
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{13}}{2*-9}=\frac{9-3\sqrt{13}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{13}}{2*-9}=\frac{9+3\sqrt{13}}{-18}
$