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(-5x+3)*(-x+6)=0

(-5x+3)*(-x+6)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(-5*x + 3)*(-x + 6) = 0
$$\left(3 - 5 x\right) \left(6 - x\right) = 0$$
Simplify
Detail solution
Expand the expression in the equation
$$\left(3 - 5 x\right) \left(6 - x\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 33 x + 18 = 0$$
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
$$a = 5$$
$$b = -33$$
$$c = 18$$
, then
D = b^2 - 4 * a * c = 

(-33)^2 - 4 * (5) * (18) = 729

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

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

or
$$x_{1} = 6$$
$$x_{2} = \frac{3}{5}$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 3/5
$$x_{1} = \frac{3}{5}$$ 
x2 = 6
$$x_{2} = 6$$ 
x2 = 6
Sum and product of roots [src] 
sum
6 + 3/5
$$\frac{3}{5} + 6$$ 
=
33/5
$$\frac{33}{5}$$ 
product
6*3
---
 5
$$\frac{3 \cdot 6}{5}$$ 
=
18/5
$$\frac{18}{5}$$ 
18/5
Numerical answer [src] 
x1 = 6.0
x2 = 0.6
x2 = 0.6
The graph
(-5x+3)*(-x+6)=0 equation
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