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14*x^2-9*x=0

14*x^2-9*x=0 equation

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Numerical solution:

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The solution

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    2          
14*x  - 9*x = 0
14x2−9x=014 x^{2} - 9 x = 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=14a = 14
b=−9b = -9
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(-9)^2 - 4 * (14) * (0) = 81

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

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

or
x1=914x_{1} = \frac{9}{14}
x2=0x_{2} = 0
Vieta's Theorem
rewrite the equation
14x2−9x=014 x^{2} - 9 x = 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
x2−9x14=0x^{2} - \frac{9 x}{14} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−914p = - \frac{9}{14}
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=914x_{1} + x_{2} = \frac{9}{14}
x1x2=0x_{1} x_{2} = 0
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-20002000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
9/14
914\frac{9}{14} 
=
9/14
914\frac{9}{14} 
product
0*9
---
 14
0⋅914\frac{0 \cdot 9}{14} 
=
0
00 
0
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 9/14
x2=914x_{2} = \frac{9}{14} 
x2 = 9/14
Numerical answer [src] 
x1 = 0.642857142857143
x2 = 0.0
x2 = 0.0
The graph
14*x^2-9*x=0 equation
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