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x^2+6*x-8=0

x^2+6*x-8=0 equation

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Numerical solution:

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The solution

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 2              
x  + 6*x - 8 = 0
$$\left(x^{2} + 6 x\right) - 8 = 0$$
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
$$a = 1$$
$$b = 6$$
$$c = -8$$
, then
D = b^2 - 4 * a * c = 

(6)^2 - 4 * (1) * (-8) = 68

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

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

or
$$x_{1} = -3 + \sqrt{17}$$
$$x_{2} = - \sqrt{17} - 3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = -8$$
The graph
Sum and product of roots [src]
sum
       ____          ____
-3 + \/ 17  + -3 - \/ 17 
$$\left(- \sqrt{17} - 3\right) + \left(-3 + \sqrt{17}\right)$$
=
-6
$$-6$$
product
/       ____\ /       ____\
\-3 + \/ 17 /*\-3 - \/ 17 /
$$\left(-3 + \sqrt{17}\right) \left(- \sqrt{17} - 3\right)$$
=
-8
$$-8$$
-8
Rapid solution [src]
            ____
x1 = -3 + \/ 17 
$$x_{1} = -3 + \sqrt{17}$$
            ____
x2 = -3 - \/ 17 
$$x_{2} = - \sqrt{17} - 3$$
x2 = -sqrt(17) - 3
Numerical answer [src]
x1 = 1.12310562561766
x2 = -7.12310562561766
x2 = -7.12310562561766
The graph
x^2+6*x-8=0 equation