1/2x+x-30+x=180

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

1/2x+x-30+x=180

We move all terms to the left:

1/2x+x-30+x-(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

2x+1/2x-210=0

We multiply all the terms by the denominator


2x*2x-210*2x+1=0

Wy multiply elements

4x^2-420x+1=0

a = 4; b = -420; c = +1;
Δ = b2-4ac
Δ = -4202-4·4·1
Δ = 176384
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:

$\sqrt{\Delta}=\sqrt{176384}=\sqrt{256*689}=\sqrt{256}*\sqrt{689}=16\sqrt{689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-16\sqrt{689}}{2*4}=\frac{420-16\sqrt{689}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+16\sqrt{689}}{2*4}=\frac{420+16\sqrt{689}}{8}
$