(1/2x)+(2x-9)+(2x)=180

Solution for (1/2x)+(2x-9)+(2x)=180 equation:

(1/2x)+(2x-9)+(2x)=180

We move all terms to the left:

(1/2x)+(2x-9)+(2x)-(180)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2x)+(2x-9)+2x-180=0

We add all the numbers together, and all the variables

2x+(+1/2x)+(2x-9)-180=0

We get rid of parentheses

2x+1/2x+2x-9-180=0

We multiply all the terms by the denominator


2x*2x+2x*2x-9*2x-180*2x+1=0

Wy multiply elements

4x^2+4x^2-18x-360x+1=0

We add all the numbers together, and all the variables

8x^2-378x+1=0

a = 8; b = -378; c = +1;
Δ = b2-4ac
Δ = -3782-4·8·1
Δ = 142852
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:

$\sqrt{\Delta}=\sqrt{142852}=\sqrt{4*35713}=\sqrt{4}*\sqrt{35713}=2\sqrt{35713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-2\sqrt{35713}}{2*8}=\frac{378-2\sqrt{35713}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+2\sqrt{35713}}{2*8}=\frac{378+2\sqrt{35713}}{16}
$