P=-X^2+56x+73

Solution for P=-X^2+56x+73 equation:

=-P^2+56P+73

We move all terms to the left:

-(-P^2+56P+73)=0

We get rid of parentheses

P^2-56P-73=0

a = 1; b = -56; c = -73;
Δ = b2-4ac
Δ = -562-4·1·(-73)
Δ = 3428
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:

$\sqrt{\Delta}=\sqrt{3428}=\sqrt{4*857}=\sqrt{4}*\sqrt{857}=2\sqrt{857}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{857}}{2*1}=\frac{56-2\sqrt{857}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{857}}{2*1}=\frac{56+2\sqrt{857}}{2}
$