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x^2+7*x+5=0 equation

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Numerical solution:

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The solution

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x  + 7*x + 5 = 0
(x2+7x)+5=0\left(x^{2} + 7 x\right) + 5 = 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=7b = 7
c=5c = 5
, then
D = b^2 - 4 * a * c = 

(7)^2 - 4 * (1) * (5) = 29

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

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

or
x1=−72+292x_{1} = - \frac{7}{2} + \frac{\sqrt{29}}{2}
x2=−72−292x_{2} = - \frac{7}{2} - \frac{\sqrt{29}}{2}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=7p = 7
q=caq = \frac{c}{a}
q=5q = 5
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−7x_{1} + x_{2} = -7
x1x2=5x_{1} x_{2} = 5
The graph
05-20-15-10-510-200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ____           ____
  7   \/ 29      7   \/ 29 
- - - ------ + - - + ------
  2     2        2     2
(−72−292)+(−72+292)\left(- \frac{7}{2} - \frac{\sqrt{29}}{2}\right) + \left(- \frac{7}{2} + \frac{\sqrt{29}}{2}\right) 
=
-7
−7-7 
product
/        ____\ /        ____\
|  7   \/ 29 | |  7   \/ 29 |
|- - - ------|*|- - + ------|
\  2     2   / \  2     2   /
(−72−292)(−72+292)\left(- \frac{7}{2} - \frac{\sqrt{29}}{2}\right) \left(- \frac{7}{2} + \frac{\sqrt{29}}{2}\right) 
=
5
55 
5
Rapid solution [src] 
             ____
       7   \/ 29 
x1 = - - - ------
       2     2
x1=−72−292x_{1} = - \frac{7}{2} - \frac{\sqrt{29}}{2} 
             ____
       7   \/ 29 
x2 = - - + ------
       2     2
x2=−72+292x_{2} = - \frac{7}{2} + \frac{\sqrt{29}}{2} 
x2 = -7/2 + sqrt(29)/2
Numerical answer [src] 
x1 = -6.19258240356725
x2 = -0.807417596432748
x2 = -0.807417596432748
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