9/2-3d=18-4d/27d

Solution for 9/2-3d=18-4d/27d equation:

9/2-3d=18-4d/27d

We move all terms to the left:

9/2-3d-(18-4d/27d)=0


Domain of the equation: 27d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

-3d-(-4d/27d+18)+9/2=0

We get rid of parentheses

-3d+4d/27d-18+9/2=0

We calculate fractions


-3d+8d/54d+243d/54d-18=0

We multiply all the terms by the denominator


-3d*54d+8d+243d-18*54d=0

We add all the numbers together, and all the variables

251d-3d*54d-18*54d=0

Wy multiply elements

-162d^2+251d-972d=0

We add all the numbers together, and all the variables

-162d^2-721d=0

a = -162; b = -721; c = 0;
Δ = b2-4ac
Δ = -7212-4·(-162)·0
Δ = 519841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{519841}=721$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-721)-721}{2*-162}=\frac{0}{-324}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-721)+721}{2*-162}=\frac{1442}{-324}
=-4+73/162
$