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

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

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

We move all terms to the left:

2x-3+1/2x+1-(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-182=0

We multiply all the terms by the denominator


2x*2x-182*2x+1=0

Wy multiply elements

4x^2-364x+1=0

a = 4; b = -364; c = +1;
Δ = b2-4ac
Δ = -3642-4·4·1
Δ = 132480
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:

$\sqrt{\Delta}=\sqrt{132480}=\sqrt{576*230}=\sqrt{576}*\sqrt{230}=24\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-364)-24\sqrt{230}}{2*4}=\frac{364-24\sqrt{230}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-364)+24\sqrt{230}}{2*4}=\frac{364+24\sqrt{230}}{8}
$