P(x)=5x^2+6x+1

Solution for P(x)=5x^2+6x+1 equation:

(P)=5P^2+6P+1

We move all terms to the left:

(P)-(5P^2+6P+1)=0

We get rid of parentheses

-5P^2+P-6P-1=0

We add all the numbers together, and all the variables

-5P^2-5P-1=0

a = -5; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·(-5)·(-1)
Δ = 5
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{-(-5)-\sqrt{5}}{2*-5}=\frac{5-\sqrt{5}}{-10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{5}}{2*-5}=\frac{5+\sqrt{5}}{-10}
$