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(8-4x)(-x+2.5)=0

(8-4x)(-x+2.5)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(8 - 4*x)*(-x + 5/2) = 0
$$\left(\frac{5}{2} - x\right) \left(8 - 4 x\right) = 0$$
Simplify
Detail solution
Expand the expression in the equation
$$\left(\frac{5}{2} - x\right) \left(8 - 4 x\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 18 x + 20 = 0$$
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
$$a = 4$$
$$b = -18$$
$$c = 20$$
, then
D = b^2 - 4 * a * c = 

(-18)^2 - 4 * (4) * (20) = 4

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

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

or
$$x_{1} = \frac{5}{2}$$
$$x_{2} = 2$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 2
$$x_{1} = 2$$ 
x2 = 5/2
$$x_{2} = \frac{5}{2}$$ 
x2 = 5/2
Sum and product of roots [src] 
sum
2 + 5/2
$$2 + \frac{5}{2}$$ 
=
9/2
$$\frac{9}{2}$$ 
product
2*5
---
 2
$$\frac{2 \cdot 5}{2}$$ 
=
5
$$5$$ 
5
Numerical answer [src] 
x1 = 2.0
x2 = 2.5
x2 = 2.5
The graph
(8-4x)(-x+2.5)=0 equation
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