x-40+2x-234+1/2x+20=180

Solution for x-40+2x-234+1/2x+20=180 equation:

x-40+2x-234+1/2x+20=180

We move all terms to the left:

x-40+2x-234+1/2x+20-(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-434=0

We multiply all the terms by the denominator


3x*2x-434*2x+1=0

Wy multiply elements

6x^2-868x+1=0

a = 6; b = -868; c = +1;
Δ = b2-4ac
Δ = -8682-4·6·1
Δ = 753400
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:

$\sqrt{\Delta}=\sqrt{753400}=\sqrt{100*7534}=\sqrt{100}*\sqrt{7534}=10\sqrt{7534}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-868)-10\sqrt{7534}}{2*6}=\frac{868-10\sqrt{7534}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-868)+10\sqrt{7534}}{2*6}=\frac{868+10\sqrt{7534}}{12}
$