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

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

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

We move all terms to the left:

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

We calculate fractions


432d^2/648d^2+(54d+5)/648d^2+108d/648d^2-6=0

We multiply all the terms by the denominator


432d^2+(54d+5)+108d-6*648d^2=0

We add all the numbers together, and all the variables

432d^2+108d+(54d+5)-6*648d^2=0

Wy multiply elements

432d^2-3888d^2+108d+(54d+5)=0

We get rid of parentheses

432d^2-3888d^2+108d+54d+5=0

We add all the numbers together, and all the variables

-3456d^2+162d+5=0

a = -3456; b = 162; c = +5;
Δ = b2-4ac
Δ = 1622-4·(-3456)·5
Δ = 95364
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:

$\sqrt{\Delta}=\sqrt{95364}=\sqrt{36*2649}=\sqrt{36}*\sqrt{2649}=6\sqrt{2649}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-6\sqrt{2649}}{2*-3456}=\frac{-162-6\sqrt{2649}}{-6912}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+6\sqrt{2649}}{2*-3456}=\frac{-162+6\sqrt{2649}}{-6912}
$