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x^2+2x-3

x^2+2x-3 equation

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Numerical solution:

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The solution

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 2              
x  + 2*x - 3 = 0
$$x^{2} + 2 x - 3 = 0$$
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
$$a = 1$$
$$b = 2$$
$$c = -3$$
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (1) * (-3) = 16

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

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

or
$$x_{1} = 1$$
Simplify
$$x_{2} = -3$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = -3$$
The graph
Rapid solution [src]
x1 = -3
$$x_{1} = -3$$
x2 = 1
$$x_{2} = 1$$
Sum and product of roots [src]
sum
0 - 3 + 1
$$\left(-3 + 0\right) + 1$$
=
-2
$$-2$$
product
1*-3*1
$$1 \left(-3\right) 1$$
=
-3
$$-3$$
-3
Numerical answer [src]
x1 = 1.0
x2 = -3.0
x2 = -3.0
The graph
x^2+2x-3 equation