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

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

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

We move all terms to the left:

5/12d+1/6d+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


We calculate fractions


(6d+5)/72d^2+12d/72d^2-6=0

We multiply all the terms by the denominator


(6d+5)+12d-6*72d^2=0

We add all the numbers together, and all the variables

12d+(6d+5)-6*72d^2=0

Wy multiply elements

-432d^2+12d+(6d+5)=0

We get rid of parentheses

-432d^2+12d+6d+5=0

We add all the numbers together, and all the variables

-432d^2+18d+5=0

a = -432; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-432)·5
Δ = 8964
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:

$\sqrt{\Delta}=\sqrt{8964}=\sqrt{36*249}=\sqrt{36}*\sqrt{249}=6\sqrt{249}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{249}}{2*-432}=\frac{-18-6\sqrt{249}}{-864}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{249}}{2*-432}=\frac{-18+6\sqrt{249}}{-864}
$