3(1/6x+9)=1/2x-27

Solution for 3(1/6x+9)=1/2x-27 equation:

3(1/6x+9)=1/2x-27

We move all terms to the left:

3(1/6x+9)-(1/2x-27)=0


Domain of the equation: 6x+9)!=0

x∈R



Domain of the equation: 2x-27)!=0

x∈R


We multiply parentheses

3x-(1/2x-27)+27=0

We get rid of parentheses

3x-1/2x+27+27=0

We multiply all the terms by the denominator


3x*2x+27*2x+27*2x-1=0

Wy multiply elements

6x^2+54x+54x-1=0

We add all the numbers together, and all the variables

6x^2+108x-1=0

a = 6; b = 108; c = -1;
Δ = b2-4ac
Δ = 1082-4·6·(-1)
Δ = 11688
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:

$\sqrt{\Delta}=\sqrt{11688}=\sqrt{4*2922}=\sqrt{4}*\sqrt{2922}=2\sqrt{2922}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-2\sqrt{2922}}{2*6}=\frac{-108-2\sqrt{2922}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+2\sqrt{2922}}{2*6}=\frac{-108+2\sqrt{2922}}{12}
$