P(6)=4x^2+6+x-6

Solution for P(6)=4x^2+6+x-6 equation:

(6)=4P^2+6+P-6

We move all terms to the left:

(6)-(4P^2+6+P-6)=0

We get rid of parentheses

-4P^2-P-6+6+6=0

We add all the numbers together, and all the variables

-4P^2-1P+6=0

a = -4; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-4)·6
Δ = 97
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{-(-1)-\sqrt{97}}{2*-4}=\frac{1-\sqrt{97}}{-8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-4}=\frac{1+\sqrt{97}}{-8}
$