Solve linear (ax + b = 0) and quadratic (ax² + bx + c = 0) equations quickly.
Equation Constants
Solving Equation
2.0000
Root x₁
The values of x that make the equation true.
Root x₂
1.0000
Equation TypeQuadratic (Real)
How Equations are Solved
Solving an equation means finding the values of the variables that satisfy the equality. For linear equations, we isolate the variable. For quadratic equations, we use the quadratic formula to find up to two roots, which may be real or complex.
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Pro Tips
If a = 0, the equation reduces to a linear one: bx + c = 0.
The 'discriminant' (b² - 4ac) tells you about the roots: >0 (2 real), =0 (1 real), <0 (2 complex).
Always check your solutions by plugging them back into the original equation.
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Fun Facts
"The quadratic formula was known to Babylonian mathematicians as early as 2000 BC, though they used words instead of symbols."
"The symbol '=' was invented by Robert Recorde in 1557 because 'no two things can be more equal than a pair of parallel lines'."
"Equations with powers of 5 or higher (quintic equations) cannot be solved by a general algebraic formula, a discovery by Évariste Galois."
