P(x)=5x2+19x+12

Solution for P(x)=5x2+19x+12 equation:

(P)=5P^2+19P+12

We move all terms to the left:

(P)-(5P^2+19P+12)=0

We get rid of parentheses

-5P^2+P-19P-12=0

We add all the numbers together, and all the variables

-5P^2-18P-12=0

a = -5; b = -18; c = -12;
Δ = b2-4ac
Δ = -182-4·(-5)·(-12)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{21}}{2*-5}=\frac{18-2\sqrt{21}}{-10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{21}}{2*-5}=\frac{18+2\sqrt{21}}{-10}
$