P(x)=x^2-7x

Solution for P(x)=x^2-7x equation:

(P)=P^2-7P

We move all terms to the left:

(P)-(P^2-7P)=0

We get rid of parentheses

-P^2+P+7P=0

We add all the numbers together, and all the variables

-1P^2+8P=0

a = -1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-1)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-1}=\frac{-16}{-2}
=+8
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-1}=\frac{0}{-2}
=0
$