P(x)=5x^2+3x-2

Solution for P(x)=5x^2+3x-2 equation:

(P)=5P^2+3P-2

We move all terms to the left:

(P)-(5P^2+3P-2)=0

We get rid of parentheses

-5P^2+P-3P+2=0

We add all the numbers together, and all the variables

-5P^2-2P+2=0

a = -5; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-5)·2
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*-5}=\frac{2-2\sqrt{11}}{-10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*-5}=\frac{2+2\sqrt{11}}{-10}
$