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x^2-x-4=0

x^2-x-4=0 equation

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Numerical solution:

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The solution

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 2            
x  - x - 4 = 0
(x2−x)−4=0\left(x^{2} - x\right) - 4 = 0
Simplify
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−1b = -1
c=−4c = -4
, then
D = b^2 - 4 * a * c = 

(-1)^2 - 4 * (1) * (-4) = 17

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=12+172x_{1} = \frac{1}{2} + \frac{\sqrt{17}}{2}
x2=12−172x_{2} = \frac{1}{2} - \frac{\sqrt{17}}{2}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−1p = -1
q=caq = \frac{c}{a}
q=−4q = -4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=1x_{1} + x_{2} = 1
x1x2=−4x_{1} x_{2} = -4
The graph
05-15-10-51015-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
           ____
     1   \/ 17 
x1 = - - ------
     2     2
x1=12−172x_{1} = \frac{1}{2} - \frac{\sqrt{17}}{2} 
           ____
     1   \/ 17 
x2 = - + ------
     2     2
x2=12+172x_{2} = \frac{1}{2} + \frac{\sqrt{17}}{2} 
x2 = 1/2 + sqrt(17)/2
Sum and product of roots [src] 
sum
      ____         ____
1   \/ 17    1   \/ 17 
- - ------ + - + ------
2     2      2     2
(12−172)+(12+172)\left(\frac{1}{2} - \frac{\sqrt{17}}{2}\right) + \left(\frac{1}{2} + \frac{\sqrt{17}}{2}\right) 
=
1
11 
product
/      ____\ /      ____\
|1   \/ 17 | |1   \/ 17 |
|- - ------|*|- + ------|
\2     2   / \2     2   /
(12−172)(12+172)\left(\frac{1}{2} - \frac{\sqrt{17}}{2}\right) \left(\frac{1}{2} + \frac{\sqrt{17}}{2}\right) 
=
-4
−4-4 
-4
Numerical answer [src] 
x1 = 2.56155281280883
x2 = -1.56155281280883
x2 = -1.56155281280883
The graph
x^2-x-4=0 equation
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