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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2P^2-3P+6=0

a = -2; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-2)·6
Δ = 57
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{-(-3)-\sqrt{57}}{2*-2}=\frac{3-\sqrt{57}}{-4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*-2}=\frac{3+\sqrt{57}}{-4}
$