-8/d+3-5/D=22/D

Solution for -8/d+3-5/D=22/D equation:

-8/d+3-5/=22/

We move all terms to the left:

-8/d+3-5/-(22/)=0


Domain of the equation: d!=0

d∈R


We add all the numbers together, and all the variables

-8/d+3-5/-(+22/)=0

We get rid of parentheses

-8/d+3-5/-22/=0

We calculate fractions


()/(d*)+(-22d-5)/(d*)+3=0

We add all the numbers together, and all the variables

()/(+d*)+(-22d-5)/(+d*)+3=0

We multiply all the terms by the denominator


(-22d-5)+3*(+d*)+()=0

We add all the numbers together, and all the variables

(-22d-5)+3*(+d*)=0

We multiply parentheses

3d^2+(-22d-5)=0

We get rid of parentheses

3d^2-22d-5=0

a = 3; b = -22; c = -5;
Δ = b2-4ac
Δ = -222-4·3·(-5)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{34}}{2*3}=\frac{22-4\sqrt{34}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{34}}{2*3}=\frac{22+4\sqrt{34}}{6}
$