180-x=1/2x+12

Solution for 180-x=1/2x+12 equation:

180-x=1/2x+12

We move all terms to the left:

180-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)+180=0

We get rid of parentheses

-1x-1/2x-12+180=0

We multiply all the terms by the denominator


-1x*2x-12*2x+180*2x-1=0

Wy multiply elements

-2x^2-24x+360x-1=0

We add all the numbers together, and all the variables

-2x^2+336x-1=0

a = -2; b = 336; c = -1;
Δ = b2-4ac
Δ = 3362-4·(-2)·(-1)
Δ = 112888
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:

$\sqrt{\Delta}=\sqrt{112888}=\sqrt{4*28222}=\sqrt{4}*\sqrt{28222}=2\sqrt{28222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-2\sqrt{28222}}{2*-2}=\frac{-336-2\sqrt{28222}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+2\sqrt{28222}}{2*-2}=\frac{-336+2\sqrt{28222}}{-4}
$