Find the whole number such that twice its square added to itself makes 10?

The formula for this is:

2x2 + x = 10

Realizing that the answer must be a small whole number, you can substitute in one of the smallest, such as 2, which works. However, if you intend to use the quadratic equation to solve this, convert the formula to

2x2 + x - 10 = 0

a = 2, b = 1, and c = -10

x = (-1 ± √(12 - (4*2*-10)) ) / 2*2

= (-1 ± √(1- -80)) / 4

= (-1 ± √81) / 4

= (-1 ± 9) / 4

= -10/4 or 8/4

Since -10/4 is -2.5 it cannot be this if it is a whole number, but it can be 8/4 which is 2.