2x+32+1/2x+65=180

Solution for 2x+32+1/2x+65=180 equation:

2x+32+1/2x+65=180

We move all terms to the left:

2x+32+1/2x+65-(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-83=0

We multiply all the terms by the denominator


2x*2x-83*2x+1=0

Wy multiply elements

4x^2-166x+1=0

a = 4; b = -166; c = +1;
Δ = b2-4ac
Δ = -1662-4·4·1
Δ = 27540
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:

$\sqrt{\Delta}=\sqrt{27540}=\sqrt{324*85}=\sqrt{324}*\sqrt{85}=18\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-18\sqrt{85}}{2*4}=\frac{166-18\sqrt{85}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+18\sqrt{85}}{2*4}=\frac{166+18\sqrt{85}}{8}
$