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(8x-11)*(-5x+17)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(8*x - 11)*(-5*x + 17) = 0
(17−5x)(8x−11)=0\left(17 - 5 x\right) \left(8 x - 11\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(17−5x)(8x−11)=0\left(17 - 5 x\right) \left(8 x - 11\right) = 0
We get the quadratic equation
−40x2+191x−187=0- 40 x^{2} + 191 x - 187 = 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=−40a = -40
b=191b = 191
c=−187c = -187
, then
D = b^2 - 4 * a * c = 

(191)^2 - 4 * (-40) * (-187) = 6561

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

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

or
x1=118x_{1} = \frac{11}{8}
x2=175x_{2} = \frac{17}{5}
The graph
2468101214161820-50005000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
11/8 + 17/5
118+175\frac{11}{8} + \frac{17}{5} 
=
191
---
 40
19140\frac{191}{40} 
product
11*17
-----
 8*5
11⋅175⋅8\frac{11 \cdot 17}{5 \cdot 8} 
=
187
---
 40
18740\frac{187}{40} 
187/40
Rapid solution [src] 
x1 = 11/8
x1=118x_{1} = \frac{11}{8} 
x2 = 17/5
x2=175x_{2} = \frac{17}{5} 
x2 = 17/5
Numerical answer [src] 
x1 = 1.375
x2 = 3.4
x2 = 3.4
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