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(3x-1)(4-5x)=0 equation

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Numerical solution:

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The solution

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(3*x - 1)*(4 - 5*x) = 0
$$\left(4 - 5 x\right) \left(3 x - 1\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(4 - 5 x\right) \left(3 x - 1\right) = 0$$
We get the quadratic equation
$$- 15 x^{2} + 17 x - 4 = 0$$
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 - it is the discriminant.
Because
$$a = -15$$
$$b = 17$$
$$c = -4$$
, then
D = b^2 - 4 * a * c = 

(17)^2 - 4 * (-15) * (-4) = 49

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

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

or
$$x_{1} = \frac{1}{3}$$
$$x_{2} = \frac{4}{5}$$
The graph
Sum and product of roots [src]
sum
1/3 + 4/5
$$\frac{1}{3} + \frac{4}{5}$$
=
17
--
15
$$\frac{17}{15}$$
product
 4 
---
3*5
$$\frac{4}{3 \cdot 5}$$
=
4/15
$$\frac{4}{15}$$
4/15
Rapid solution [src]
x1 = 1/3
$$x_{1} = \frac{1}{3}$$
x2 = 4/5
$$x_{2} = \frac{4}{5}$$
x2 = 4/5
Numerical answer [src]
x1 = 0.8
x2 = 0.333333333333333
x2 = 0.333333333333333