d+4/2d+2=34

Solution for d+4/2d+2=34 equation:

d+4/2d+2=34

We move all terms to the left:

d+4/2d+2-(34)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

d+4/2d-32=0

We multiply all the terms by the denominator


d*2d-32*2d+4=0

Wy multiply elements

2d^2-64d+4=0

a = 2; b = -64; c = +4;
Δ = b2-4ac
Δ = -642-4·2·4
Δ = 4064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4064}=\sqrt{16*254}=\sqrt{16}*\sqrt{254}=4\sqrt{254}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{254}}{2*2}=\frac{64-4\sqrt{254}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{254}}{2*2}=\frac{64+4\sqrt{254}}{4}
$