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-x^2+8x+6=0

-x^2+8x+6=0 equation

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Numerical solution:

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The solution

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   2              
- x  + 8*x + 6 = 0
−x2+8x+6=0- x^{2} + 8 x + 6 = 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=6c = 6
, then
D = b^2 - 4 * a * c = 

(8)^2 - 4 * (-1) * (6) = 88

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

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

or
x1=4−22x_{1} = 4 - \sqrt{22}
Simplify
x2=4+22x_{2} = 4 + \sqrt{22}
Simplify
Vieta's Theorem
rewrite the equation
−x2+8x+6=0- x^{2} + 8 x + 6 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−8x−6=0x^{2} - 8 x - 6 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−8p = -8
q=caq = \frac{c}{a}
q=−6q = -6
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=8x_{1} + x_{2} = 8
x1x2=−6x_{1} x_{2} = -6
The graph
05-15-10-510152025-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
          ____         ____
0 + 4 - \/ 22  + 4 + \/ 22
((4−22)+0)+(4+22)\left(\left(4 - \sqrt{22}\right) + 0\right) + \left(4 + \sqrt{22}\right) 
=
8
88 
product
  /      ____\ /      ____\
1*\4 - \/ 22 /*\4 + \/ 22 /
1⋅(4−22)(4+22)1 \cdot \left(4 - \sqrt{22}\right) \left(4 + \sqrt{22}\right) 
=
-6
−6-6 
-6
Rapid solution [src] 
           ____
x1 = 4 - \/ 22
x1=4−22x_{1} = 4 - \sqrt{22}
Simplify 
           ____
x2 = 4 + \/ 22
x2=4+22x_{2} = 4 + \sqrt{22}
Simplify
Numerical answer [src] 
x1 = -0.69041575982343
x2 = 8.69041575982343
x2 = 8.69041575982343
The graph
-x^2+8x+6=0 equation
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