5/2d-d=3+3/2d

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

5/2d-d=3+3/2d

We move all terms to the left:

5/2d-d-(3+3/2d)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 2d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

5/2d-d-(3/2d+3)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1d*2d-3*2d+5-3=0

We add all the numbers together, and all the variables

-1d*2d-3*2d+2=0

Wy multiply elements

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

a = -2; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-2)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-2}=\frac{6-2\sqrt{13}}{-4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-2}=\frac{6+2\sqrt{13}}{-4}
$