P(x)=3X^2-10x+3

Solution for P(x)=3X^2-10x+3 equation:

(P)=3P^2-10P+3

We move all terms to the left:

(P)-(3P^2-10P+3)=0

We get rid of parentheses

-3P^2+P+10P-3=0

We add all the numbers together, and all the variables

-3P^2+11P-3=0

a = -3; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·(-3)·(-3)
Δ = 85
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{-(11)-\sqrt{85}}{2*-3}=\frac{-11-\sqrt{85}}{-6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{85}}{2*-3}=\frac{-11+\sqrt{85}}{-6}
$