1/2x+x+30=180

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

1/2x+x+30=180

We move all terms to the left:

1/2x+x+30-(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

x+1/2x-150=0

We multiply all the terms by the denominator


x*2x-150*2x+1=0

Wy multiply elements

2x^2-300x+1=0

a = 2; b = -300; c = +1;
Δ = b2-4ac
Δ = -3002-4·2·1
Δ = 89992
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:

$\sqrt{\Delta}=\sqrt{89992}=\sqrt{4*22498}=\sqrt{4}*\sqrt{22498}=2\sqrt{22498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22498}}{2*2}=\frac{300-2\sqrt{22498}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22498}}{2*2}=\frac{300+2\sqrt{22498}}{4}
$