How to use: Solve quadratic equations in the form ax² + bx + c = 0 using the quadratic formula. Enter coefficients a, b, and c (numbers in front of x², x, and constant term). Results show the solution(s) for x. Formula: x = [-b ± √(b² - 4ac)] / 2a. Example: For 2x² + 5x + 3 = 0, enter a=2, b=5, c=3 → solutions x=-1 and x=-1.5. Applications: physics motion equations, engineering optimization, profit maximization, projectile trajectories. Discriminant (b²-4ac): positive = 2 real solutions, zero = 1 solution, negative = complex solutions. Essential for algebra, calculus, and advanced mathematics.