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(x-13)*(x+8)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(x - 13)*(x + 8) = 0
(x−13)(x+8)=0\left(x - 13\right) \left(x + 8\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(x−13)(x+8)=0\left(x - 13\right) \left(x + 8\right) = 0
We get the quadratic equation
x2−5x−104=0x^{2} - 5 x - 104 = 0
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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−5b = -5
c=−104c = -104
, then
D = b^2 - 4 * a * c = 

(-5)^2 - 4 * (1) * (-104) = 441

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

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

or
x1=13x_{1} = 13
x2=−8x_{2} = -8
Rapid solution [src] 
x1 = -8
x1=−8x_{1} = -8 
x2 = 13
x2=13x_{2} = 13 
x2 = 13
Sum and product of roots [src] 
sum
-8 + 13
−8+13-8 + 13 
=
5
55 
product
-8*13
−104- 104 
=
-104
−104-104 
-104
Numerical answer [src] 
x1 = -8.0
x2 = 13.0
x2 = 13.0
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