P(x)=x^2-40x+50

Solution for P(x)=x^2-40x+50 equation:

(P)=P^2-40P+50

We move all terms to the left:

(P)-(P^2-40P+50)=0

We get rid of parentheses

-P^2+P+40P-50=0

We add all the numbers together, and all the variables

-1P^2+41P-50=0

a = -1; b = 41; c = -50;
Δ = b2-4ac
Δ = 412-4·(-1)·(-50)
Δ = 1481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-\sqrt{1481}}{2*-1}=\frac{-41-\sqrt{1481}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1481}}{2*-1}=\frac{-41+\sqrt{1481}}{-2}
$