A linear equation of the form ax + b = 0 is solved by moving b to the right side and dividing by a. The solution is x = -b/a. For example: 2x + 6 = 0 gives x = -3.

Use the quadratic formula: for ax² + bx + c = 0, x = (-b ± √(b²-4ac)) / 2a. The discriminant D = b²-4ac determines the number of solutions: D > 0 gives two real solutions, D = 0 gives one, D < 0 gives no real solutions.

The discriminant D = b² - 4ac (for equation ax² + bx + c = 0). If D > 0 there are two real solutions, D = 0 gives one double root, and D < 0 means no real solutions.