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9x^2=27x

9x^2=27x equation

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Numerical solution:

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The solution

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   2       
9*x  = 27*x
9x2=27x9 x^{2} = 27 x
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
9x2=27x9 x^{2} = 27 x
to
9x2−27x=09 x^{2} - 27 x = 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=−27b = -27
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(-27)^2 - 4 * (9) * (0) = 729

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

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

or
x1=3x_{1} = 3
x2=0x_{2} = 0
Vieta's Theorem
rewrite the equation
9x2=27x9 x^{2} = 27 x
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−3x=0x^{2} - 3 x = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−3p = -3
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=3x_{1} + x_{2} = 3
x1x2=0x_{1} x_{2} = 0
The graph
02468-8-6-4-21012-10-20002000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 3
x2=3x_{2} = 3 
x2 = 3
Sum and product of roots [src] 
sum
3
33 
=
3
33 
product
0*3
0⋅30 \cdot 3 
=
0
00 
0
Numerical answer [src] 
x1 = 3.0
x2 = 0.0
x2 = 0.0
The graph
9x^2=27x equation
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