50+2x+1/2x=180

Solution for 50+2x+1/2x=180 equation:

50+2x+1/2x=180

We move all terms to the left:

50+2x+1/2x-(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

2x+1/2x-130=0

We multiply all the terms by the denominator


2x*2x-130*2x+1=0

Wy multiply elements

4x^2-260x+1=0

a = 4; b = -260; c = +1;
Δ = b2-4ac
Δ = -2602-4·4·1
Δ = 67584
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:

$\sqrt{\Delta}=\sqrt{67584}=\sqrt{1024*66}=\sqrt{1024}*\sqrt{66}=32\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-32\sqrt{66}}{2*4}=\frac{260-32\sqrt{66}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+32\sqrt{66}}{2*4}=\frac{260+32\sqrt{66}}{8}
$