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x^2+3*x-9=0

x^2+3*x-9=0 equation

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Numerical solution:

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The solution

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 2              
x  + 3*x - 9 = 0
$$\left(x^{2} + 3 x\right) - 9 = 0$$
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
$$a = 1$$
$$b = 3$$
$$c = -9$$
, then
D = b^2 - 4 * a * c = 

(3)^2 - 4 * (1) * (-9) = 45

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

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

or
$$x_{1} = - \frac{3}{2} + \frac{3 \sqrt{5}}{2}$$
$$x_{2} = - \frac{3 \sqrt{5}}{2} - \frac{3}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = -9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = -9$$
The graph
Sum and product of roots [src]
sum
          ___             ___
  3   3*\/ 5      3   3*\/ 5 
- - + ------- + - - - -------
  2      2        2      2   
$$\left(- \frac{3 \sqrt{5}}{2} - \frac{3}{2}\right) + \left(- \frac{3}{2} + \frac{3 \sqrt{5}}{2}\right)$$
=
-3
$$-3$$
product
/          ___\ /          ___\
|  3   3*\/ 5 | |  3   3*\/ 5 |
|- - + -------|*|- - - -------|
\  2      2   / \  2      2   /
$$\left(- \frac{3}{2} + \frac{3 \sqrt{5}}{2}\right) \left(- \frac{3 \sqrt{5}}{2} - \frac{3}{2}\right)$$
=
-9
$$-9$$
-9
Rapid solution [src]
               ___
       3   3*\/ 5 
x1 = - - + -------
       2      2   
$$x_{1} = - \frac{3}{2} + \frac{3 \sqrt{5}}{2}$$
               ___
       3   3*\/ 5 
x2 = - - - -------
       2      2   
$$x_{2} = - \frac{3 \sqrt{5}}{2} - \frac{3}{2}$$
x2 = -3*sqrt(5)/2 - 3/2
Numerical answer [src]
x1 = 1.85410196624968
x2 = -4.85410196624968
x2 = -4.85410196624968
The graph
x^2+3*x-9=0 equation