3(1/2x+9)=x-12+1/2x

Solution for 3(1/2x+9)=x-12+1/2x equation:

3(1/2x+9)=x-12+1/2x

We move all terms to the left:

3(1/2x+9)-(x-12+1/2x)=0


Domain of the equation: 2x+9)!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(1/2x+9)-(x+1/2x-12)=0

We multiply parentheses

3x-(x+1/2x-12)+27=0

We get rid of parentheses

3x-x-1/2x+12+27=0

We multiply all the terms by the denominator


3x*2x-x*2x+12*2x+27*2x-1=0

Wy multiply elements

6x^2-2x^2+24x+54x-1=0

We add all the numbers together, and all the variables

4x^2+78x-1=0

a = 4; b = 78; c = -1;
Δ = b2-4ac
Δ = 782-4·4·(-1)
Δ = 6100
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:

$\sqrt{\Delta}=\sqrt{6100}=\sqrt{100*61}=\sqrt{100}*\sqrt{61}=10\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-10\sqrt{61}}{2*4}=\frac{-78-10\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+10\sqrt{61}}{2*4}=\frac{-78+10\sqrt{61}}{8}
$