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3*x^2-4*x=0

3*x^2-4*x=0 equation

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Numerical solution:

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The solution

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

(-4)^2 - 4 * (3) * (0) = 16

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

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

or
x1=43x_{1} = \frac{4}{3}
Simplify
x2=0x_{2} = 0
Simplify
Vieta's Theorem
rewrite the equation
3x2−4x=03 x^{2} - 4 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
x2−4x3=0x^{2} - \frac{4 x}{3} = 0
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=−43p = - \frac{4}{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=43x_{1} + x_{2} = \frac{4}{3}
x1x2=0x_{1} x_{2} = 0
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0
Simplify 
x2 = 4/3
x2=43x_{2} = \frac{4}{3}
Simplify
Sum and product of roots [src] 
sum
0 + 0 + 4/3
(0+0)+43\left(0 + 0\right) + \frac{4}{3} 
=
4/3
43\frac{4}{3} 
product
1*0*4/3
1⋅0⋅431 \cdot 0 \cdot \frac{4}{3} 
=
0
00 
0
Numerical answer [src] 
x1 = 0.0
x2 = 1.33333333333333
x2 = 1.33333333333333
The graph
3*x^2-4*x=0 equation
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