P(x)=x2-5x-300

Solution for P(x)=x2-5x-300 equation:

(P)=P2-5P-300

We move all terms to the left:

(P)-(P2-5P-300)=0

We add all the numbers together, and all the variables

-(+P^2-5P-300)+P=0

We get rid of parentheses

-P^2+5P+P+300=0

We add all the numbers together, and all the variables

-1P^2+6P+300=0

a = -1; b = 6; c = +300;
Δ = b2-4ac
Δ = 62-4·(-1)·300
Δ = 1236
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:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{309}}{2*-1}=\frac{-6-2\sqrt{309}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{309}}{2*-1}=\frac{-6+2\sqrt{309}}{-2}
$