One way of solving quadratic equations is to use the technique of "completing the square" to rearrange the quadratic into something like a "(squared part) equals (a number)" format. For example:

Step 1: 4x² – 2x – 5 = 0

Step 2: 4x² – 2x = 5

Step 3: x² – 1/2 x = 5/4

Step 4: x² – 1/2 x + 1/16 = 5/4 + 1/16

Step 5: (x – 1/4)² = 21/16

Step 6: 

Step 7: