2x=180-135+1/2x

Solution for 2x=180-135+1/2x equation:

2x=180-135+1/2x

We move all terms to the left:

2x-(180-135+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(1/2x+45)=0

We get rid of parentheses

2x-1/2x-45=0

We multiply all the terms by the denominator


2x*2x-45*2x-1=0

Wy multiply elements

4x^2-90x-1=0

a = 4; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·4·(-1)
Δ = 8116
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:

$\sqrt{\Delta}=\sqrt{8116}=\sqrt{4*2029}=\sqrt{4}*\sqrt{2029}=2\sqrt{2029}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2029}}{2*4}=\frac{90-2\sqrt{2029}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2029}}{2*4}=\frac{90+2\sqrt{2029}}{8}
$