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7x^2+18*x+5=0 equation

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The solution

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7*x  + 18*x + 5 = 0
(7x2+18x)+5=0\left(7 x^{2} + 18 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=7a = 7
b=18b = 18
c=5c = 5
, then
D = b^2 - 4 * a * c = 

(18)^2 - 4 * (7) * (5) = 184

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

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

or
x1=−97+467x_{1} = - \frac{9}{7} + \frac{\sqrt{46}}{7}
x2=−97−467x_{2} = - \frac{9}{7} - \frac{\sqrt{46}}{7}
Vieta's Theorem
rewrite the equation
(7x2+18x)+5=0\left(7 x^{2} + 18 x\right) + 5 = 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+18x7+57=0x^{2} + \frac{18 x}{7} + \frac{5}{7} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=187p = \frac{18}{7}
q=caq = \frac{c}{a}
q=57q = \frac{5}{7}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−187x_{1} + x_{2} = - \frac{18}{7}
x1x2=57x_{1} x_{2} = \frac{5}{7}
The graph
05-15-10-510-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ____           ____
  9   \/ 46      9   \/ 46 
- - - ------ + - - + ------
  7     7        7     7
(−97−467)+(−97+467)\left(- \frac{9}{7} - \frac{\sqrt{46}}{7}\right) + \left(- \frac{9}{7} + \frac{\sqrt{46}}{7}\right) 
=
-18/7
−187- \frac{18}{7} 
product
/        ____\ /        ____\
|  9   \/ 46 | |  9   \/ 46 |
|- - - ------|*|- - + ------|
\  7     7   / \  7     7   /
(−97−467)(−97+467)\left(- \frac{9}{7} - \frac{\sqrt{46}}{7}\right) \left(- \frac{9}{7} + \frac{\sqrt{46}}{7}\right) 
=
5/7
57\frac{5}{7} 
5/7
Rapid solution [src] 
             ____
       9   \/ 46 
x1 = - - - ------
       7     7
x1=−97−467x_{1} = - \frac{9}{7} - \frac{\sqrt{46}}{7} 
             ____
       9   \/ 46 
x2 = - - + ------
       7     7
x2=−97+467x_{2} = - \frac{9}{7} + \frac{\sqrt{46}}{7} 
x2 = -9/7 + sqrt(46)/7
Numerical answer [src] 
x1 = -0.316810002410676
x2 = -2.2546185690179
x2 = -2.2546185690179
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