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

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

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

We move all terms to the left:

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


Domain of the equation: 12d!=0

d!=0/12

d!=0

d∈R



Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R


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

We calculate fractions


432d^2/648d^2+270d/648d^2+108d/648d^2-6=0

We multiply all the terms by the denominator


432d^2+270d+108d-6*648d^2=0

We add all the numbers together, and all the variables

432d^2+378d-6*648d^2=0

Wy multiply elements

432d^2-3888d^2+378d=0

We add all the numbers together, and all the variables

-3456d^2+378d=0

a = -3456; b = 378; c = 0;
Δ = b2-4ac
Δ = 3782-4·(-3456)·0
Δ = 142884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{142884}=378$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(378)-378}{2*-3456}=\frac{-756}{-6912}
=7/64
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(378)+378}{2*-3456}=\frac{0}{-6912}
=0
$