Answer:

4x² = 9      (x - 3)(x + 4) = 0      2x² - 5x + 2 = 0 are examples of quadratic equations, for they can all be written in the form ax² + bx + c = 0 where a ≠ 0. They each have two solutions, which can be found in a variety of ways

first dividing by 4 to get x² = 9/4.
From which x = 3/2 or x = -3/2.
In the second example, as the product of the two factors (x - 3) and (x + 4) is zero, then either x - 3 = 0 or x + 4 = 0, from which x = 3 or x = -4

In the third example, 2x² - 5x + 2 = 0 can be factorised to give (2x - 1)(x - 2) = 0.
But factors are not always easy to spot so a quadratic equation can be solved by the method known as completing the square, illustrated here by solving x² + 8x + 5 = 0