X-30+2x-120+1/2x-20=180

Solution for X-30+2x-120+1/2x-20=180 equation:

X-30+2X-120+1/2X-20=180

We move all terms to the left:

X-30+2X-120+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-350=0

We multiply all the terms by the denominator


3X*2X-350*2X+1=0

Wy multiply elements

6X^2-700X+1=0

a = 6; b = -700; c = +1;
Δ = b2-4ac
Δ = -7002-4·6·1
Δ = 489976
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:

$\sqrt{\Delta}=\sqrt{489976}=\sqrt{4*122494}=\sqrt{4}*\sqrt{122494}=2\sqrt{122494}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{122494}}{2*6}=\frac{700-2\sqrt{122494}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{122494}}{2*6}=\frac{700+2\sqrt{122494}}{12}
$