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

Solution for (5/2)d-3/2=-1/2 equation:

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

We move all terms to the left:

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


Domain of the equation: 2)d!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5d^2*2-2=0

Wy multiply elements

10d^2-2=0

a = 10; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·10·(-2)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*10}=\frac{0-4\sqrt{5}}{20}
=-\frac{4\sqrt{5}}{20}
=-\frac{\sqrt{5}}{5}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*10}=\frac{0+4\sqrt{5}}{20}
=\frac{4\sqrt{5}}{20}
=\frac{\sqrt{5}}{5}
$