P(x)=x2+15x+14

Solution for P(x)=x2+15x+14 equation:

(P)=P2+15P+14

We move all terms to the left:

(P)-(P2+15P+14)=0

We add all the numbers together, and all the variables

-(+P^2+15P+14)+P=0

We get rid of parentheses

-P^2-15P+P-14=0

We add all the numbers together, and all the variables

-1P^2-14P-14=0

a = -1; b = -14; c = -14;
Δ = b2-4ac
Δ = -142-4·(-1)·(-14)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{35}}{2*-1}=\frac{14-2\sqrt{35}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{35}}{2*-1}=\frac{14+2\sqrt{35}}{-2}
$