x+(1/2x-3)=180

Solution for x+(1/2x-3)=180 equation:

x+(1/2x-3)=180

We move all terms to the left:

x+(1/2x-3)-(180)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

x+1/2x-3-180=0

We multiply all the terms by the denominator


x*2x-3*2x-180*2x+1=0

Wy multiply elements

2x^2-6x-360x+1=0

We add all the numbers together, and all the variables

2x^2-366x+1=0

a = 2; b = -366; c = +1;
Δ = b2-4ac
Δ = -3662-4·2·1
Δ = 133948
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:

$\sqrt{\Delta}=\sqrt{133948}=\sqrt{4*33487}=\sqrt{4}*\sqrt{33487}=2\sqrt{33487}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-366)-2\sqrt{33487}}{2*2}=\frac{366-2\sqrt{33487}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-366)+2\sqrt{33487}}{2*2}=\frac{366+2\sqrt{33487}}{4}
$