To solve a quadratic you need to first factorise it

This can be done by putting it into two sets of brackets like (x+p)(x+q)

Quadratic equations always occour in the form Ax² + Bx + C

Where A, B, and C are constants

This will expand to x² + px + qx + pq

Or by collecting like terms x² + (p+q)x + pq

Therefore the numbers in the brackets must add to give B and multiply to give C

To solve a quadratic

Find factors of C that add to B

Subsititute out into brackets

Eg

x² + 18x + 80

Factors of 80 1,80 2,20 4,20 5,16 8,10

8+10 = 18 therefore (x+8)(x+10)

To check we can expand the brackets

x²+8x + 10x + 80

x²+18x + 80

Therefore our factorisation was correct