Identify the logic of the below given series and given

I. x² – 12x + 32 = 0

II. y² + y - 20 = 0

I. 2y²– 19y + 35 = 0

II. 4x²– 16x + 15 = 0

I. 20y² - 13y + 2 = 0

II. 6x² - 25x + 14 = 0

l. 3x² + 17x + 24 = 0

II. 2y² + 15y + 27 = 0

I. 5x² -14x + 8 = 0   

II. 2y² + 17y  + 36 = 0    

I: 3x² - 18x + 24 = 0

II: 5y² + 10y - 15 = 0

I. 2 x² - 15 + 18 = 0

II. x²- 3 + 2 = 0

I. 15y²+ 26y + 8 = 0

II. 20x²+ 7x – 6 = 0

Solve the quadratic equations and determine the relation between x and y:

Equation 1: x² - 24x + 143 = 0

Equation 2: y² - 20y + 96 = 0

I. 6p² – 7p = 5p – 7p² + 25

II. 11q² – 63q + 90 = 0