5d+28=1/d+9d-2

Solution for 5d+28=1/d+9d-2 equation:

5d+28=1/d+9d-2

We move all terms to the left:

5d+28-(1/d+9d-2)=0


Domain of the equation: d+9d-2)!=0

d∈R


We add all the numbers together, and all the variables

5d-(9d+1/d-2)+28=0

We get rid of parentheses

5d-9d-1/d+2+28=0

We multiply all the terms by the denominator


5d*d-9d*d+2*d+28*d-1=0

We add all the numbers together, and all the variables

30d+5d*d-9d*d-1=0

Wy multiply elements

5d^2-9d^2+30d-1=0

We add all the numbers together, and all the variables

-4d^2+30d-1=0

a = -4; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·(-4)·(-1)
Δ = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{221}}{2*-4}=\frac{-30-2\sqrt{221}}{-8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{221}}{2*-4}=\frac{-30+2\sqrt{221}}{-8}
$