3/2d+18=1d-3

Solution for 3/2d+18=1d-3 equation:

3/2d+18=1d-3

We move all terms to the left:

3/2d+18-(1d-3)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

3/2d-(d-3)+18=0

We get rid of parentheses

3/2d-d+3+18=0

We multiply all the terms by the denominator


-d*2d+3*2d+18*2d+3=0

Wy multiply elements

-2d^2+6d+36d+3=0

We add all the numbers together, and all the variables

-2d^2+42d+3=0

a = -2; b = 42; c = +3;
Δ = b2-4ac
Δ = 422-4·(-2)·3
Δ = 1788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{447}}{2*-2}=\frac{-42-2\sqrt{447}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{447}}{2*-2}=\frac{-42+2\sqrt{447}}{-4}
$