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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2P^2-2P+2=0

a = -2; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-2)·2
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*-2}=\frac{2-2\sqrt{5}}{-4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*-2}=\frac{2+2\sqrt{5}}{-4}
$