2(x+8)=11/2x+20

Solution for 2(x+8)=11/2x+20 equation:

2(x+8)=11/2x+20

We move all terms to the left:

2(x+8)-(11/2x+20)=0


Domain of the equation: 2x+20)!=0

x∈R


We multiply parentheses

2x-(11/2x+20)+16=0

We get rid of parentheses

2x-11/2x-20+16=0

We multiply all the terms by the denominator


2x*2x-20*2x+16*2x-11=0

Wy multiply elements

4x^2-40x+32x-11=0

We add all the numbers together, and all the variables

4x^2-8x-11=0

a = 4; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·4·(-11)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*4}=\frac{8-4\sqrt{15}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*4}=\frac{8+4\sqrt{15}}{8}
$