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x^2-3x-28=0

x^2-3x-28=0 equation

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Numerical solution:

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The solution

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 2               
x  - 3*x - 28 = 0
$$\left(x^{2} - 3 x\right) - 28 = 0$$
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
$$a = 1$$
$$b = -3$$
$$c = -28$$
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (-28) = 121

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

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

or
$$x_{1} = 7$$
$$x_{2} = -4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -28$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = -28$$
The graph
Sum and product of roots [src]
sum
-4 + 7
$$-4 + 7$$
=
3
$$3$$
product
-4*7
$$- 28$$
=
-28
$$-28$$
-28
Rapid solution [src]
x1 = -4
$$x_{1} = -4$$
x2 = 7
$$x_{2} = 7$$
x2 = 7
Numerical answer [src]
x1 = 7.0
x2 = -4.0
x2 = -4.0
The graph
x^2-3x-28=0 equation