45/p+p=18

Solution for 45/p+p=18 equation:

45/p+p=18

We move all terms to the left:

45/p+p-(18)=0


Domain of the equation: p!=0

p∈R


We add all the numbers together, and all the variables

p+45/p-18=0

We multiply all the terms by the denominator


p*p-18*p+45=0

We add all the numbers together, and all the variables

-18p+p*p+45=0

Wy multiply elements

p^2-18p+45=0

a = 1; b = -18; c = +45;
Δ = b2-4ac
Δ = -182-4·1·45
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*1}=\frac{6}{2}
=3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*1}=\frac{30}{2}
=15
$