Choose a quadratic equation that you want to solve. For example, solve the quadratic equation x^2 + 3x = -2.
Rearrange the equation into the standard form, which is ax^2 + bx + c = 0. In the standard form, a and b represent the coefficients in front of the variable and c represents the constant number. In the example, add 2 to both sides of the equation to move -2 to the left side, which results in x^2 + 3x + 2 = -2 + 2. This leaves x^2 + 3x + 2 = 0.
Determine the numbers in the quadratic equation that represent a, b and c. In the example, 1, 3 and 2 represent a, b, and c, respectively.
Plug the numbers for a, b and c into the quadratic formula. In the example, this yields the quadratic formula x = [-3 +/- sqrt(3^2 - 4(1)(2))]/[2(1)]. In the formula, sqrt represents square root.
Square b inside the square root sign. In the example, square 3 to get 9.
Multiply 4 by a by c inside the square root sign. In the example, multiply 4 by 1 by 2, which equals 8.
Subtract the result of 4ac from the result of b^2 inside the square root sign. In the example, subtract 8 from 9, which equals 1. This leaves x = [-3 +/- sqrt(1)]/[2(1)].
Calculate the square root of the number in the square root sign. In the example, calculate the square root of 1, which equals 1. This leaves x = (-3 +/- 1)/[2(1)].
Multiply 2 by a in the denominator. In the example, multiply 2 by 1, which equals 2. This leaves x = (-3 +/- 1)/2.
Separate the formula into two formulas -- one with a "+" sign in the numerator and one with a "-" sign -- to separate the +/- sign in the numerator. This means the equation will have two solutions. In the example, this results in x = (-3 + 1)/2 and x = (-3 - 1)/2.
Add the numbers in the numerator of the first equation. In the example, add -3 to 1, which equals -2. This leaves x = -2/2.
Divide the numerator by the denominator to solve for x. In the example, divide -2 by 2, which equals -1. This leaves x = -1, which means -1 is the first solution.
Subtract the numbers in the numerator of the second equation. In the example, subtract 1 from -3, which equals -4. This leaves x = -4/2.
Divide the numerator by the denominator to solve for x. In the example, divide -4 by 2, which equals -2. This leaves x = -2, which means -2 is the second solution. So the solutions to the quadratic equation are -1 and -2.