x+2x-1-1/2x+4=180

Solution for x+2x-1-1/2x+4=180 equation:

x+2x-1-1/2x+4=180

We move all terms to the left:

x+2x-1-1/2x+4-(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

3x-1/2x-177=0

We multiply all the terms by the denominator


3x*2x-177*2x-1=0

Wy multiply elements

6x^2-354x-1=0

a = 6; b = -354; c = -1;
Δ = b2-4ac
Δ = -3542-4·6·(-1)
Δ = 125340
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:

$\sqrt{\Delta}=\sqrt{125340}=\sqrt{4*31335}=\sqrt{4}*\sqrt{31335}=2\sqrt{31335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-354)-2\sqrt{31335}}{2*6}=\frac{354-2\sqrt{31335}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-354)+2\sqrt{31335}}{2*6}=\frac{354+2\sqrt{31335}}{12}
$