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9*x-72/x=-18 equation

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Numerical solution:

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The solution

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      72      
9*x - -- = -18
      x
9x−72x=−189 x - \frac{72}{x} = -18
Simplify
Detail solution
Given the equation:
9x−72x=−189 x - \frac{72}{x} = -18
Multiply the equation sides by the denominators:
and x
we get:
x(9x−72x)=−18xx \left(9 x - \frac{72}{x}\right) = - 18 x
9x2−72=−18x9 x^{2} - 72 = - 18 x
Move right part of the equation to
left part with negative sign.

The equation is transformed from
9x2−72=−18x9 x^{2} - 72 = - 18 x
to
9x2+18x−72=09 x^{2} + 18 x - 72 = 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=9a = 9
b=18b = 18
c=−72c = -72
, then
D = b^2 - 4 * a * c = 

(18)^2 - 4 * (9) * (-72) = 2916

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=−4x_{2} = -4
The graph
05-20-15-10-51015-200000200000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -4
x1=−4x_{1} = -4 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Sum and product of roots [src] 
sum
-4 + 2
−4+2-4 + 2 
=
-2
−2-2 
product
-4*2
−8- 8 
=
-8
−8-8 
-8
Numerical answer [src] 
x1 = 2.0
x2 = -4.0
x2 = -4.0
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