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x^2+4*x-5=0

x^2+4*x-5=0 equation

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Numerical solution:

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The solution

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 2              
x  + 4*x - 5 = 0
$$\left(x^{2} + 4 x\right) - 5 = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 4$$
$$c = -5$$
, then
D = b^2 - 4 * a * c = 

(4)^2 - 4 * (1) * (-5) = 36

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

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

or
$$x_{1} = 1$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -5$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-5 + 1
$$-5 + 1$$ 
=
-4
$$-4$$ 
product
-5
$$-5$$ 
=
-5
$$-5$$ 
-5
Rapid solution [src] 
x1 = -5
$$x_{1} = -5$$ 
x2 = 1
$$x_{2} = 1$$ 
x2 = 1
Numerical answer [src] 
x1 = 1.0
x2 = -5.0
x2 = -5.0
The graph
x^2+4*x-5=0 equation
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