P(x)=x2-12x-160

Solution for P(x)=x2-12x-160 equation:

(P)=P2-12P-160

We move all terms to the left:

(P)-(P2-12P-160)=0

We add all the numbers together, and all the variables

-(+P^2-12P-160)+P=0

We get rid of parentheses

-P^2+12P+P+160=0

We add all the numbers together, and all the variables

-1P^2+13P+160=0

a = -1; b = 13; c = +160;
Δ = b2-4ac
Δ = 132-4·(-1)·160
Δ = 809
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{-(13)-\sqrt{809}}{2*-1}=\frac{-13-\sqrt{809}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{809}}{2*-1}=\frac{-13+\sqrt{809}}{-2}
$