Quadratic equations solver calculator
Calculator finds out solution of quadratic equation given in general ax²+bx+c=0 form.

Beta version

This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !

Input equation, which you want to solve

Parameters of the ax2 + bx + c = 0 equation
Coefficient a
(just before x2)
Coefficient b
(just before x)
Free parameter c

The solution of your equation

The equation you entered
Show source2x2+5x8=02\cdot{ x}^{2}+5\cdot x - 8 = 0
The solution of the equation
Show sourcex{54894,54+894} x \in \left\{\frac{-5}{4}-\frac{\sqrt{89}}{4}, \frac{-5}{4}+\frac{\sqrt{89}}{4}\right\}

The solution step-by-step

I. We calculatate discriminant of the quadratic equation Δ\Delta.
Δ=52(42(8))=25(42(8))=25(64)==25+64=89\begin{aligned}\Delta& = {5}^{2} - \left(4\cdot2\cdot\left(-8\right)\right) = 25 - \left(4\cdot2\cdot\left(-8\right)\right) = 25 - \left(-64\right) = \\ & = 25+64 = 89\end{aligned}
II. Delta is positive (Δ > 0), so equation has two solutions (roots).
The first solution is:
x1=58922=5894=54894\begin{aligned}x_1& = \frac{-5 - \sqrt{89}}{2\cdot2} = \frac{-5 - \sqrt{89}}{4} = \frac{-5}{4}-\frac{\sqrt{89}}{4}\end{aligned}The second solution is:
x2=5+8922=5+894=54+894\begin{aligned}x_2& = \frac{-5+\sqrt{89}}{2\cdot2} = \frac{-5+\sqrt{89}}{4} = \frac{-5}{4}+\frac{\sqrt{89}}{4}\end{aligned}

Some facts

  • The quadratic equation is an equation that can be presented in the form:
    a x2+b x+c=0a~x^2 + b~x + c = 0
    • a, b, c - constant parameters, these are numbers that we know,
    • x - unknown variable, it's a number, which we search for.
  • Quadratic equation can have one solution, two solutions or do not have solutions.
  • The universal method of solving quadratic equations uses discriminant of the quadratic polynomial (so-called delta):
    Δ=b24 a c \Delta={ b}^{2}-4~ a~ c
  • When we calculate the discriminant, three scenarios are possible:
    • discriminant is positive (Δ > 0) - equation has two different solutions (two different roots):
      x1=bΔ2 a x_1=\frac{- b-\sqrt{ \Delta}}{2~ a}
      x2=b+Δ2 a x_2=\frac{- b+\sqrt{ \Delta}}{2~ a}
    • discriminant is zero (Δ = 0) - equation has exactly one solution (so-called double root):
      h=b2 a h=\frac{- b}{2~ a}
    • discriminant is negative (Δ < 0) - equation has no solutions (so-called contradictory equation).

Tags and links to this website

What tags this calculator has


This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

Links to external sites (leaving Calculla?)

JavaScript failed !
So this is static version of this website.
This website works a lot better in JavaScript enabled browser.
Please enable JavaScript.