1/6d+2/3=1/4d-5

Solution for 1/6d+2/3=1/4d-5 equation:

1/6d+2/3=1/4d-5

We move all terms to the left:

1/6d+2/3-(1/4d-5)=0


Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R



Domain of the equation: 4d-5)!=0

d∈R


We get rid of parentheses

1/6d-1/4d+5+2/3=0

We calculate fractions


192d^2/216d^2+36d/216d^2+(-54d)/216d^2+5=0

We multiply all the terms by the denominator


192d^2+36d+(-54d)+5*216d^2=0

Wy multiply elements

192d^2+1080d^2+36d+(-54d)=0

We get rid of parentheses

192d^2+1080d^2+36d-54d=0

We add all the numbers together, and all the variables

1272d^2-18d=0

a = 1272; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·1272·0
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*1272}=\frac{0}{2544}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*1272}=\frac{36}{2544}
=3/212
$