1/2x+(x+36)=180

Solution for 1/2x+(x+36)=180 equation:

1/2x+(x+36)=180

We move all terms to the left:

1/2x+(x+36)-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+x+36-180=0

We multiply all the terms by the denominator


x*2x+36*2x-180*2x+1=0

Wy multiply elements

2x^2+72x-360x+1=0

We add all the numbers together, and all the variables

2x^2-288x+1=0

a = 2; b = -288; c = +1;
Δ = b2-4ac
Δ = -2882-4·2·1
Δ = 82936
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:

$\sqrt{\Delta}=\sqrt{82936}=\sqrt{4*20734}=\sqrt{4}*\sqrt{20734}=2\sqrt{20734}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-2\sqrt{20734}}{2*2}=\frac{288-2\sqrt{20734}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+2\sqrt{20734}}{2*2}=\frac{288+2\sqrt{20734}}{4}
$