5/12+1/6d+1/3D+1/12d=6

Solution for 5/12+1/6d+1/3D+1/12d=6 equation:

5/12+1/6d+1/3+1/12d=6

We move all terms to the left:

5/12+1/6d+1/3+1/12d-(6)=0


Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R



Domain of the equation: 12d!=0

d!=0/12

d!=0

d∈R


determiningTheFunctionDomain
1/6d+1/12d-6+5/12+1/3=0

We calculate fractions


864d^2/2592d^2+432d/2592d^2+54d/2592d^2+270d/2592d^2-6=0

We multiply all the terms by the denominator


864d^2+432d+54d+270d-6*2592d^2=0

We add all the numbers together, and all the variables

864d^2+756d-6*2592d^2=0

Wy multiply elements

864d^2-15552d^2+756d=0

We add all the numbers together, and all the variables

-14688d^2+756d=0

a = -14688; b = 756; c = 0;
Δ = b2-4ac
Δ = 7562-4·(-14688)·0
Δ = 571536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{571536}=756$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-756}{2*-14688}=\frac{-1512}{-29376}
=7/136
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+756}{2*-14688}=\frac{0}{-29376}
=0
$