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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-1)·2
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*-1}=\frac{2-2\sqrt{3}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*-1}=\frac{2+2\sqrt{3}}{-2}
$