(5/12)*d+(1/6)*d+(1/3)*d+(1/12)*d=6

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

(5/12)*d+(1/6)*d+(1/3)*d+(1/12)*d=6

We move all terms to the left:

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


Domain of the equation: 12)*d!=0

d!=0/1

d!=0

d∈R



Domain of the equation: 6)*d!=0

d!=0/1

d!=0

d∈R



Domain of the equation: 3)*d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

8d^2-6=0

a = 8; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·8·(-6)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*8}=\frac{0-8\sqrt{3}}{16}
=-\frac{8\sqrt{3}}{16}
=-\frac{\sqrt{3}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*8}=\frac{0+8\sqrt{3}}{16}
=\frac{8\sqrt{3}}{16}
=\frac{\sqrt{3}}{2}
$