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

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Numerical solution:

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The solution

You have entered [src] 
(5*x - 2)*(x + 3) = 0
(x+3)(5x−2)=0\left(x + 3\right) \left(5 x - 2\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(x+3)(5x−2)=0\left(x + 3\right) \left(5 x - 2\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) = 289

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

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

or
x1=25x_{1} = \frac{2}{5}
x2=−3x_{2} = -3
The graph
05-15-10-51015-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -3
x1=−3x_{1} = -3 
x2 = 2/5
x2=25x_{2} = \frac{2}{5} 
x2 = 2/5
Sum and product of roots [src] 
sum
-3 + 2/5
−3+25-3 + \frac{2}{5} 
=
-13/5
−135- \frac{13}{5} 
product
-3*2
----
 5
−65- \frac{6}{5} 
=
-6/5
−65- \frac{6}{5} 
-6/5
Numerical answer [src] 
x1 = 0.4
x2 = -3.0
x2 = -3.0
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