p*5p=4.5

Solution for p*5p=4.5 equation:

p*5p=4.5

We move all terms to the left:

p*5p-(4.5)=0

We add all the numbers together, and all the variables

p*5p-4.5=0

Wy multiply elements

5p^2-4.5=0

a = 5; b = 0; c = -4.5;
Δ = b2-4ac
Δ = 02-4·5·(-4.5)
Δ = 90
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{10}}{2*5}=\frac{0-3\sqrt{10}}{10}
=-\frac{3\sqrt{10}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{10}}{2*5}=\frac{0+3\sqrt{10}}{10}
=\frac{3\sqrt{10}}{10}
$