The quadratic equation is most often used to solve curves on a graph when an object is experiencing projectile motion. The sides of the curve intersect the xaxis twice and yaxis once. The two answers the equation yields are the xaxis intersectioning points. The equation uses coefficients, a number multipied by a variable, and is equal to zero. Once you plug in your known values for the coefficients, you can solve for x.
Set Up the Equation

Write the quadratic equation on a piece of paper. If you are solving for "x," the equation should read x = (b ± √((b^2)4ac)))/2a. The equation yields two answers for "x," corresponding to their location on the xaxis. The equation reads "x" equals the opposite of "b" plus or minus the square root of "b" squared minus 4 times "a" times "c" divided by 2 times "a." Also write the values you know about your curve; for example, if "a" equals 3, "b" equals 20 and "c" equals 10. Plug your known values into the quadratic equation. Using the example numbers given, you have x = (5 ± √((20^2)(4x3x10)))/(2x3).
Solve the Equation

Solve the equation according to the order of operations to obtain a value for "x." Solve the value that is squared first and the numbers that are multiplied by each other second. The example now reads x = (5 ± √(400120))/6. Solve the subraction before solving for the square root phrases in the equation. The example now reads x = (5 ± 16.73)/6.
Reaching the Answer

Solve for "x" by adding or subtracting the numbers on the top of the equation and dividing it by the number on the bottom. The equation uses a ± sign, read plus or minus sign, because the equation needs to yield two values. The two values represent where the two sides of the curve intersect the xaxis on a graph. The answers to the example problem are x = 3.62 and x = 1.96.
Plot the Points

On a graph, the first value is to the left of the yaxis on the negative side of the xaxis; the second value is to the right of the yaxis, on the positive side. Having these values enables you to solve for other properties of the curve, such as area.
References
 Photo Credit Jupiterimages/Photos.com/Getty Images