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Quadratic Formula Calculator
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Example: 2x^2-5x-3=0
Step-By-Step Example
Learn step-by-step how to use the quadratic formula!
Example (Click to try)
2x2−5x−3=0
About the quadratic formula
Solve an equation of the form ax2+bx+c=0 by using the quadratic formula:
x=
−b±√b2−4ac
2a
Quadratic Formula Video Lesson
Solve with the Quadratic Formula Step-by-Step [1:29]
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Step-by-Step Examples
Algebra
Quadratic Equations
Find the Quadratic Equation Given the Roots
Step 1
and are the two real distinct solutions for the quadratic equation, which means that and are the factors of the quadratic equation.
Step 2
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Step 3
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Move to the left of .
Rewrite as .
Multiply by .
Subtract from .
Step 4
The standard quadratic equation using the given set of solutions is .
Step 5
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We can help you solve an equation of the form "ax2 + bx + c = 0"
Just enter the values of a, b and c below:
algebra/images/quadratic-solver.js
Is it Quadratic?
Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.
The name comes from "quad" meaning square, as the variable is squared (in other words x2).
These are all quadratic equations in disguise:
x2 = 3x -1 | x2 - 3x + 1 = 0 | a=1, b=-3, c=1 |
2(x2 - 2x) = 5 | 2x2 - 4x - 5 = 0 | a=2, b=-4, c=-5 |
x(x-1) = 3 | x2 - x - 3 = 0 | a=1, b=-1, c=-3 |
5 + 1/x - 1/x2 = 0 | 5x2 + x - 1 = 0 | a=5, b=1, c=-1 |
How Does this Work?
The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:
The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !
The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer:
- when it is positive, we get two real solutions,
- when it is zero we get just ONE solution,
- when it is negative we get complex solutions.
Learn more at Quadratic Equations
Note: you can still access the old version here.