11/2x+20+2(x+8)+21/2x-6=180

Solution for 11/2x+20+2(x+8)+21/2x-6=180 equation:

11/2x+20+2(x+8)+21/2x-6=180

We move all terms to the left:

11/2x+20+2(x+8)+21/2x-6-(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

11/2x+2(x+8)+21/2x-166=0

We multiply parentheses

11/2x+2x+21/2x+16-166=0

We multiply all the terms by the denominator


2x*2x+16*2x-166*2x+11+21=0

We add all the numbers together, and all the variables

2x*2x+16*2x-166*2x+32=0

Wy multiply elements

4x^2+32x-332x+32=0

We add all the numbers together, and all the variables

4x^2-300x+32=0

a = 4; b = -300; c = +32;
Δ = b2-4ac
Δ = -3002-4·4·32
Δ = 89488
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:

$\sqrt{\Delta}=\sqrt{89488}=\sqrt{16*5593}=\sqrt{16}*\sqrt{5593}=4\sqrt{5593}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{5593}}{2*4}=\frac{300-4\sqrt{5593}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{5593}}{2*4}=\frac{300+4\sqrt{5593}}{8}
$