2(d+12)=1/2d

Solution for 2(d+12)=1/2d equation:

2(d+12)=1/2d

We move all terms to the left:

2(d+12)-(1/2d)=0


Domain of the equation: 2d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

2(d+12)-(+1/2d)=0

We multiply parentheses

2d-(+1/2d)+24=0

We get rid of parentheses

2d-1/2d+24=0

We multiply all the terms by the denominator


2d*2d+24*2d-1=0

Wy multiply elements

4d^2+48d-1=0

a = 4; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·4·(-1)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{145}}{2*4}=\frac{-48-4\sqrt{145}}{8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{145}}{2*4}=\frac{-48+4\sqrt{145}}{8}
$