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x^2-8x-7=0 equation

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Numerical solution:

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The solution

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 2              
x  - 8*x - 7 = 0
(x2−8x)−7=0\left(x^{2} - 8 x\right) - 7 = 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=−7c = -7
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (1) * (-7) = 92

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

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

or
x1=4+23x_{1} = 4 + \sqrt{23}
x2=4−23x_{2} = 4 - \sqrt{23}
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=−7q = -7
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=8x_{1} + x_{2} = 8
x1x2=−7x_{1} x_{2} = -7
The graph
05-15-10-510152025-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
      ____         ____
4 - \/ 23  + 4 + \/ 23
(4−23)+(4+23)\left(4 - \sqrt{23}\right) + \left(4 + \sqrt{23}\right) 
=
8
88 
product
/      ____\ /      ____\
\4 - \/ 23 /*\4 + \/ 23 /
(4−23)(4+23)\left(4 - \sqrt{23}\right) \left(4 + \sqrt{23}\right) 
=
-7
−7-7 
-7
Rapid solution [src] 
           ____
x1 = 4 - \/ 23
x1=4−23x_{1} = 4 - \sqrt{23} 
           ____
x2 = 4 + \/ 23
x2=4+23x_{2} = 4 + \sqrt{23} 
x2 = 4 + sqrt(23)
Numerical answer [src] 
x1 = 8.79583152331272
x2 = -0.79583152331272
x2 = -0.79583152331272
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