x-24+2x-165+1/2x+12=180

Solution for x-24+2x-165+1/2x+12=180 equation:

x-24+2x-165+1/2x+12=180

We move all terms to the left:

x-24+2x-165+1/2x+12-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-357=0

We multiply all the terms by the denominator


3x*2x-357*2x+1=0

Wy multiply elements

6x^2-714x+1=0

a = 6; b = -714; c = +1;
Δ = b2-4ac
Δ = -7142-4·6·1
Δ = 509772
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:

$\sqrt{\Delta}=\sqrt{509772}=\sqrt{4*127443}=\sqrt{4}*\sqrt{127443}=2\sqrt{127443}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-714)-2\sqrt{127443}}{2*6}=\frac{714-2\sqrt{127443}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-714)+2\sqrt{127443}}{2*6}=\frac{714+2\sqrt{127443}}{12}
$