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(5x-3)(x-2)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(5*x - 3)*(x - 2) = 0
(x−2)(5x−3)=0\left(x - 2\right) \left(5 x - 3\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(x−2)(5x−3)=0\left(x - 2\right) \left(5 x - 3\right) = 0
We get the quadratic equation
5x2−13x+6=05 x^{2} - 13 x + 6 = 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:
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=5a = 5
b=−13b = -13
c=6c = 6
, then
D = b^2 - 4 * a * c = 

(-13)^2 - 4 * (5) * (6) = 49

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

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

or
x1=2x_{1} = 2
x2=35x_{2} = \frac{3}{5}
The graph
05-10-51015-5001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
2 + 3/5
35+2\frac{3}{5} + 2 
=
13/5
135\frac{13}{5} 
product
2*3
---
 5
2⋅35\frac{2 \cdot 3}{5} 
=
6/5
65\frac{6}{5} 
6/5
Rapid solution [src] 
x1 = 3/5
x1=35x_{1} = \frac{3}{5} 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Numerical answer [src] 
x1 = 0.6
x2 = 2.0
x2 = 2.0
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