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3*x^2-2*x=0

3*x^2-2*x=0 equation

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Numerical solution:

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The solution

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   2          
3*x  - 2*x = 0
3x2−2x=03 x^{2} - 2 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=3a = 3
b=−2b = -2
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (3) * (0) = 4

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

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

or
x1=23x_{1} = \frac{2}{3}
x2=0x_{2} = 0
Vieta's Theorem
rewrite the equation
3x2−2x=03 x^{2} - 2 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
x2−2x3=0x^{2} - \frac{2 x}{3} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−23p = - \frac{2}{3}
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=23x_{1} + x_{2} = \frac{2}{3}
x1x2=0x_{1} x_{2} = 0
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 2/3
x2=23x_{2} = \frac{2}{3} 
x2 = 2/3
Sum and product of roots [src] 
sum
2/3
23\frac{2}{3} 
=
2/3
23\frac{2}{3} 
product
0*2
---
 3
0⋅23\frac{0 \cdot 2}{3} 
=
0
00 
0
Numerical answer [src] 
x1 = 0.0
x2 = 0.666666666666667
x2 = 0.666666666666667
The graph
3*x^2-2*x=0 equation
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