P(x)=3x^2+9x^2-12x

Solution for P(x)=3x^2+9x^2-12x equation:

(P)=3P^2+9P^2-12P

We move all terms to the left:

(P)-(3P^2+9P^2-12P)=0

We get rid of parentheses

-3P^2-9P^2+12P+P=0

We add all the numbers together, and all the variables

-12P^2+13P=0

a = -12; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-12)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-12}=\frac{-26}{-24}
=1+1/12
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-12}=\frac{0}{-24}
=0
$