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x^2-8x-84=0 equation

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Numerical solution:

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The solution

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x  - 8*x - 84 = 0
(x2−8x)−84=0\left(x^{2} - 8 x\right) - 84 = 0
Simplify
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:
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=−8b = -8
c=−84c = -84
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (1) * (-84) = 400

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

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

or
x1=14x_{1} = 14
x2=−6x_{2} = -6
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−8p = -8
q=caq = \frac{c}{a}
q=−84q = -84
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=8x_{1} + x_{2} = 8
x1x2=−84x_{1} x_{2} = -84
Sum and product of roots [src] 
sum
-6 + 14
−6+14-6 + 14 
=
8
88 
product
-6*14
−84- 84 
=
-84
−84-84 
-84
Rapid solution [src] 
x1 = -6
x1=−6x_{1} = -6 
x2 = 14
x2=14x_{2} = 14 
x2 = 14
Numerical answer [src] 
x1 = 14.0
x2 = -6.0
x2 = -6.0
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