6-x=1/2x+12

Solution for 6-x=1/2x+12 equation:

6-x=1/2x+12

We move all terms to the left:

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


Domain of the equation: 2x+12)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-1x-1/2x-12+6=0

We multiply all the terms by the denominator


-1x*2x-12*2x+6*2x-1=0

Wy multiply elements

-2x^2-24x+12x-1=0

We add all the numbers together, and all the variables

-2x^2-12x-1=0

a = -2; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-2)·(-1)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*-2}=\frac{12-2\sqrt{34}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*-2}=\frac{12+2\sqrt{34}}{-4}
$