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x^2+5x-4=0 equation

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Numerical solution:

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The solution

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x  + 5*x - 4 = 0
(x2+5x)−4=0\left(x^{2} + 5 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=5b = 5
c=−4c = -4
, then
D = b^2 - 4 * a * c = 

(5)^2 - 4 * (1) * (-4) = 41

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

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

or
x1=−52+412x_{1} = - \frac{5}{2} + \frac{\sqrt{41}}{2}
x2=−412−52x_{2} = - \frac{\sqrt{41}}{2} - \frac{5}{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=5p = 5
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=−5x_{1} + x_{2} = -5
x1x2=−4x_{1} x_{2} = -4
The graph
05-20-15-10-51015-200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ____           ____
  5   \/ 41      5   \/ 41 
- - + ------ + - - - ------
  2     2        2     2
(−412−52)+(−52+412)\left(- \frac{\sqrt{41}}{2} - \frac{5}{2}\right) + \left(- \frac{5}{2} + \frac{\sqrt{41}}{2}\right) 
=
-5
−5-5 
product
/        ____\ /        ____\
|  5   \/ 41 | |  5   \/ 41 |
|- - + ------|*|- - - ------|
\  2     2   / \  2     2   /
(−52+412)(−412−52)\left(- \frac{5}{2} + \frac{\sqrt{41}}{2}\right) \left(- \frac{\sqrt{41}}{2} - \frac{5}{2}\right) 
=
-4
−4-4 
-4
Rapid solution [src] 
             ____
       5   \/ 41 
x1 = - - + ------
       2     2
x1=−52+412x_{1} = - \frac{5}{2} + \frac{\sqrt{41}}{2} 
             ____
       5   \/ 41 
x2 = - - - ------
       2     2
x2=−412−52x_{2} = - \frac{\sqrt{41}}{2} - \frac{5}{2} 
x2 = -sqrt(41)/2 - 5/2
Numerical answer [src] 
x1 = 0.701562118716424
x2 = -5.70156211871642
x2 = -5.70156211871642
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