1/2x+x=180-x

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

1/2x+x=180-x

We move all terms to the left:

1/2x+x-(180-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+x-(-1x+180)=0

We add all the numbers together, and all the variables

x+1/2x-(-1x+180)=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-360x+1=0

a = 4; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·4·1
Δ = 129584
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:

$\sqrt{\Delta}=\sqrt{129584}=\sqrt{16*8099}=\sqrt{16}*\sqrt{8099}=4\sqrt{8099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8099}}{2*4}=\frac{360-4\sqrt{8099}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8099}}{2*4}=\frac{360+4\sqrt{8099}}{8}
$