P(x)=x2-3x-4

Solution for P(x)=x2-3x-4 equation:

(P)=P2-3P-4

We move all terms to the left:

(P)-(P2-3P-4)=0

We add all the numbers together, and all the variables

-(+P^2-3P-4)+P=0

We get rid of parentheses

-P^2+3P+P+4=0

We add all the numbers together, and all the variables

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

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$