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5*x-4/7*x^2=0

5*x-4/7*x^2=0 equation

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Numerical solution:

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The solution

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         2    
      4*x     
5*x - ---- = 0
       7      
$$- \frac{4 x^{2}}{7} + 5 x = 0$$
Detail solution
Expand the expression in the equation
$$\left(- \frac{4 x^{2}}{7} + 5 x\right) + 0 = 0$$
We get the quadratic equation
$$- \frac{4 x^{2}}{7} + 5 x = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = - \frac{4}{7}$$
$$b = 5$$
$$c = 0$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) \left(\left(- \frac{4}{7}\right) 4\right) 0 + 5^{2} = 25$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 0$$
Simplify
$$x_{2} = \frac{35}{4}$$
Simplify
Vieta's Theorem
rewrite the equation
$$- \frac{4 x^{2}}{7} + 5 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{35 x}{4} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{35}{4}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{35}{4}$$
$$x_{1} x_{2} = 0$$
The graph
Sum and product of roots [src]
sum
0 + 35/4
$$\left(0\right) + \left(\frac{35}{4}\right)$$
=
35/4
$$\frac{35}{4}$$
product
0 * 35/4
$$\left(0\right) * \left(\frac{35}{4}\right)$$
=
0
$$0$$
Rapid solution [src]
x_1 = 0
$$x_{1} = 0$$
x_2 = 35/4
$$x_{2} = \frac{35}{4}$$
Numerical answer [src]
x1 = 8.75
x2 = 0.0
x2 = 0.0
The graph
5*x-4/7*x^2=0 equation