7/12d+3=1/6d

Solution for 7/12d+3=1/6d equation:

7/12d+3=1/6d

We move all terms to the left:

7/12d+3-(1/6d)=0


Domain of the equation: 12d!=0

d!=0/12

d!=0

d∈R



Domain of the equation: 6d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

7/12d-(+1/6d)+3=0

We get rid of parentheses

7/12d-1/6d+3=0

We calculate fractions


42d/72d^2+(-12d)/72d^2+3=0

We multiply all the terms by the denominator


42d+(-12d)+3*72d^2=0

Wy multiply elements

216d^2+42d+(-12d)=0

We get rid of parentheses

216d^2+42d-12d=0

We add all the numbers together, and all the variables

216d^2+30d=0

a = 216; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·216·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*216}=\frac{-60}{432}
=-5/36
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*216}=\frac{0}{432}
=0
$