3(1/6x+9)=1/2x-24

Solution for 3(1/6x+9)=1/2x-24 equation:

3(1/6x+9)=1/2x-24

We move all terms to the left:

3(1/6x+9)-(1/2x-24)=0


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

x∈R



Domain of the equation: 2x-24)!=0

x∈R


We multiply parentheses

3x-(1/2x-24)+27=0

We get rid of parentheses

3x-1/2x+24+27=0

We multiply all the terms by the denominator


3x*2x+24*2x+27*2x-1=0

Wy multiply elements

6x^2+48x+54x-1=0

We add all the numbers together, and all the variables

6x^2+102x-1=0

a = 6; b = 102; c = -1;
Δ = b2-4ac
Δ = 1022-4·6·(-1)
Δ = 10428
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:

$\sqrt{\Delta}=\sqrt{10428}=\sqrt{4*2607}=\sqrt{4}*\sqrt{2607}=2\sqrt{2607}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-2\sqrt{2607}}{2*6}=\frac{-102-2\sqrt{2607}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+2\sqrt{2607}}{2*6}=\frac{-102+2\sqrt{2607}}{12}
$