45=(p-2)(p-2)

Solution for 45=(p-2)(p-2) equation:

45=(p-2)(p-2)

We move all terms to the left:

45-((p-2)(p-2))=0

We multiply parentheses ..

-((+p^2-2p-2p+4))+45=0


We calculate terms in parentheses: -((+p^2-2p-2p+4)), so:

(+p^2-2p-2p+4)

We get rid of parentheses

p^2-2p-2p+4

We add all the numbers together, and all the variables

p^2-4p+4

Back to the equation:

-(p^2-4p+4)


We get rid of parentheses

-p^2+4p-4+45=0

We add all the numbers together, and all the variables

-1p^2+4p+41=0

a = -1; b = 4; c = +41;
Δ = b2-4ac
Δ = 42-4·(-1)·41
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{5}}{2*-1}=\frac{-4-6\sqrt{5}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{5}}{2*-1}=\frac{-4+6\sqrt{5}}{-2}
$