Algebra 2 Calculator

Write it as you would on paper. Implicit multiplication such as 2x and 3(x - 1) is understood. With no "=" sign the input is collected and evaluated instead of solved.
Only used when no exact method applies. Roots outside this window are not reported.
Solution
-3
Algebra Calculator
Number of real solutions
2
Kind of equation
quadratic
Standard form
2x^2 + 5x - 3 = 0
Factored form
2(x + 3)(x - 1/2)
How it was solved
exact: rational-root theorem and exact division, then numeric roots of the remaining factor
Worked out from OpenStax, Elementary Algebra 2e, chapters 2 and 9: solving linear equations and quadratic equations and 2 other sources.

How this is worked out

8 steps
  1. Bring everything to one side: 2x^2 + 5x - 3 = 0
  2. Read off a = 2, b = 5, c = -3.
  3. Discriminant b² - 4ac = 5² - 4(2)((-3)) = 49.
  4. The discriminant is positive, so there are two distinct real roots.
  5. Quadratic formula x = (-b ± √(b² - 4ac)) / (2a) = ((-5) ± √49) / 4.
  6. Factored: 2(x + 3)(x - 1/2) = 0
  7. Check x = -3: substituting back leaves left - right = 0.
  8. Check x = 1/2: substituting back leaves left - right = 0.
Solutionstable
x = -3, x = 1/2
Check by substitutiontable
x = -3: left - right = 0, x = 1/2: left - right = 0

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