1/6d+2/3=1/4d+2

Solution for 1/6d+2/3=1/4d+2 equation:

1/6d+2/3=1/4d+2

We move all terms to the left:

1/6d+2/3-(1/4d+2)=0


Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R



Domain of the equation: 4d+2)!=0

d∈R


We get rid of parentheses

1/6d-1/4d-2+2/3=0

We calculate fractions


192d^2/216d^2+36d/216d^2+(-54d)/216d^2-2=0

We multiply all the terms by the denominator


192d^2+36d+(-54d)-2*216d^2=0

Wy multiply elements

192d^2-432d^2+36d+(-54d)=0

We get rid of parentheses

192d^2-432d^2+36d-54d=0

We add all the numbers together, and all the variables

-240d^2-18d=0

a = -240; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-240)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-240}=\frac{0}{-480}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-240}=\frac{36}{-480}
=-3/40
$