2x+6=4/2x+16

Solution for 2x+6=4/2x+16 equation:

2x+6=4/2x+16

We move all terms to the left:

2x+6-(4/2x+16)=0


Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

2x-4/2x-16+6=0

We multiply all the terms by the denominator


2x*2x-16*2x+6*2x-4=0

Wy multiply elements

4x^2-32x+12x-4=0

We add all the numbers together, and all the variables

4x^2-20x-4=0

a = 4; b = -20; c = -4;
Δ = b2-4ac
Δ = -202-4·4·(-4)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{29}}{2*4}=\frac{20-4\sqrt{29}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{29}}{2*4}=\frac{20+4\sqrt{29}}{8}
$