5+1.50p+0.50=30/p

Solution for 5+1.50p+0.50=30/p equation:

5+1.50p+0.50=30/p

We move all terms to the left:

5+1.50p+0.50-(30/p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1.50p-(+30/p)+5+0.50=0

We add all the numbers together, and all the variables

1.50p-(+30/p)+5.5=0

We get rid of parentheses

1.50p-30/p+5.5=0

We multiply all the terms by the denominator


(1.50p)*p+(5.5)*p-30=0

We add all the numbers together, and all the variables

(+1.50p)*p+(5.5)*p-30=0

We multiply parentheses

p^2+5.5p-30=0

a = 1; b = 5.5; c = -30;
Δ = b2-4ac
Δ = 5.52-4·1·(-30)
Δ = 150.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5.5)-\sqrt{150.25}}{2*1}=\frac{-5.5-\sqrt{150.25}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.5)+\sqrt{150.25}}{2*1}=\frac{-5.5+\sqrt{150.25}}{2}
$