1/5p+9/p+6=30

Solution for 1/5p+9/p+6=30 equation:

1/5p+9/p+6=30

We move all terms to the left:

1/5p+9/p+6-(30)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: p!=0

p∈R


We add all the numbers together, and all the variables

1/5p+9/p-24=0

We calculate fractions


p/5p^2+45p/5p^2-24=0

We multiply all the terms by the denominator


p+45p-24*5p^2=0

We add all the numbers together, and all the variables

46p-24*5p^2=0

Wy multiply elements

-120p^2+46p=0

a = -120; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-120)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-120}=\frac{-92}{-240}
=23/60
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-120}=\frac{0}{-240}
=0
$