12(6-x)+3x=1/2x-8

Solution for 12(6-x)+3x=1/2x-8 equation:

12(6-x)+3x=1/2x-8

We move all terms to the left:

12(6-x)+3x-(1/2x-8)=0


Domain of the equation: 2x-8)!=0

x∈R


We add all the numbers together, and all the variables

12(-1x+6)+3x-(1/2x-8)=0

We add all the numbers together, and all the variables

3x+12(-1x+6)-(1/2x-8)=0

We multiply parentheses

3x-12x-(1/2x-8)+72=0

We get rid of parentheses

3x-12x-1/2x+8+72=0

We multiply all the terms by the denominator


3x*2x-12x*2x+8*2x+72*2x-1=0

Wy multiply elements

6x^2-24x^2+16x+144x-1=0

We add all the numbers together, and all the variables

-18x^2+160x-1=0

a = -18; b = 160; c = -1;
Δ = b2-4ac
Δ = 1602-4·(-18)·(-1)
Δ = 25528
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:

$\sqrt{\Delta}=\sqrt{25528}=\sqrt{4*6382}=\sqrt{4}*\sqrt{6382}=2\sqrt{6382}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-2\sqrt{6382}}{2*-18}=\frac{-160-2\sqrt{6382}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+2\sqrt{6382}}{2*-18}=\frac{-160+2\sqrt{6382}}{-36}
$