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If you have an equation

ax²+bx+c = 0

the roots of the equation are found by the formula:

The expression b² - 4ac is called the discriminant . Its value tells you whether you have no roots, 1 root or 2 roots.
Case 1: b² - 4ac <0
If it is less than 0, that means you are trying to find the square root of a negative number. Ergo, no roots. An example is x²-2x+5 .
Case 2: b² - 4ac = 0
The square root of 0 is 0. One root. Period. An example is x²-2x+1 . The only root is x = 1 .
Case 2: b² - 4ac > 0
Here we have 2 roots. An example is 2x²-x-15 . We have a = 2 , b = -1 and c = -15 . Plugging these numbers into the formula, one root is 3 and the other is -5/2.