5/6d-9=1/3d+11

Solution for 5/6d-9=1/3d+11 equation:

5/6d-9=1/3d+11

We move all terms to the left:

5/6d-9-(1/3d+11)=0


Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R



Domain of the equation: 3d+11)!=0

d∈R


We get rid of parentheses

5/6d-1/3d-11-9=0

We calculate fractions


15d/18d^2+(-6d)/18d^2-11-9=0

We add all the numbers together, and all the variables

15d/18d^2+(-6d)/18d^2-20=0

We multiply all the terms by the denominator


15d+(-6d)-20*18d^2=0

Wy multiply elements

-360d^2+15d+(-6d)=0

We get rid of parentheses

-360d^2+15d-6d=0

We add all the numbers together, and all the variables

-360d^2+9d=0

a = -360; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-360)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-360}=\frac{-18}{-720}
=1/40
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-360}=\frac{0}{-720}
=0
$