1=-2.5p^2+550p

Solution for 1=-2.5p^2+550p equation:

1=-2.5p^2+550p

We move all terms to the left:

1-(-2.5p^2+550p)=0

We get rid of parentheses

2.5p^2-550p+1=0

a = 2.5; b = -550; c = +1;
Δ = b2-4ac
Δ = -5502-4·2.5·1
Δ = 302490
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:

$\sqrt{\Delta}=\sqrt{302490}=\sqrt{9*33610}=\sqrt{9}*\sqrt{33610}=3\sqrt{33610}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-550)-3\sqrt{33610}}{2*2.5}=\frac{550-3\sqrt{33610}}{5}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-550)+3\sqrt{33610}}{2*2.5}=\frac{550+3\sqrt{33610}}{5}
$