15+2x+1/2x=180

Solution for 15+2x+1/2x=180 equation:

15+2x+1/2x=180

We move all terms to the left:

15+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-165=0

We multiply all the terms by the denominator


2x*2x-165*2x+1=0

Wy multiply elements

4x^2-330x+1=0

a = 4; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·4·1
Δ = 108884
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:

$\sqrt{\Delta}=\sqrt{108884}=\sqrt{4*27221}=\sqrt{4}*\sqrt{27221}=2\sqrt{27221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27221}}{2*4}=\frac{330-2\sqrt{27221}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27221}}{2*4}=\frac{330+2\sqrt{27221}}{8}
$