4x^{2} = 9 (x - 3)(x + 4) = 0
2x^{2} - 5x + 2 = 0 are examples of quadratic equations, for they
can all be written in the form ax^{2} + 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 x^{2} = 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,
2x^{2} - 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 x^{2} + 8x + 5 = 0