P(x)=x^2-6x-4

Solution for P(x)=x^2-6x-4 equation:

(P)=P^2-6P-4

We move all terms to the left:

(P)-(P^2-6P-4)=0

We get rid of parentheses

-P^2+P+6P+4=0

We add all the numbers together, and all the variables

-1P^2+7P+4=0

a = -1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·(-1)·4
Δ = 65
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{-(7)-\sqrt{65}}{2*-1}=\frac{-7-\sqrt{65}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*-1}=\frac{-7+\sqrt{65}}{-2}
$