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-x^2+8x+6=0

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

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Numerical solution:

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The solution

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

(8)^2 - 4 * (-1) * (6) = 88

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

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

or
$$x_{1} = 4 - \sqrt{22}$$
Simplify
$$x_{2} = 4 + \sqrt{22}$$
Simplify
Vieta's Theorem
rewrite the equation
$$- x^{2} + 8 x + 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 8 x - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = -6$$
The graph
Sum and product of roots [src]
sum
          ____         ____
0 + 4 - \/ 22  + 4 + \/ 22 
$$\left(\left(4 - \sqrt{22}\right) + 0\right) + \left(4 + \sqrt{22}\right)$$
=
8
$$8$$
product
  /      ____\ /      ____\
1*\4 - \/ 22 /*\4 + \/ 22 /
$$1 \cdot \left(4 - \sqrt{22}\right) \left(4 + \sqrt{22}\right)$$
=
-6
$$-6$$
-6
Rapid solution [src]
           ____
x1 = 4 - \/ 22 
$$x_{1} = 4 - \sqrt{22}$$
           ____
x2 = 4 + \/ 22 
$$x_{2} = 4 + \sqrt{22}$$
Numerical answer [src]
x1 = -0.69041575982343
x2 = 8.69041575982343
x2 = 8.69041575982343
The graph
-x^2+8x+6=0 equation