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1/3x^2-27=0

1/3x^2-27=0 equation

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Numerical solution:

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The solution

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 2         
x          
-- - 27 = 0
3
x23−27=0\frac{x^{2}}{3} - 27 = 0
Simplify
Detail solution
Expand the expression in the equation
(x23−27)+0=0\left(\frac{x^{2}}{3} - 27\right) + 0 = 0
We get the quadratic equation
x23−27=0\frac{x^{2}}{3} - 27 = 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=13a = \frac{1}{3}
b=0b = 0
c=−27c = -27
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1/3) * (-27) = 36

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

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

or
x1=9x_{1} = 9
Simplify
x2=−9x_{2} = -9
Simplify
Vieta's Theorem
rewrite the equation
x23−27=0\frac{x^{2}}{3} - 27 = 0
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
x2−81=0x^{2} - 81 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−81q = -81
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−81x_{1} x_{2} = -81
The graph
05-25-20-15-10-510152025-100100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
0 - 9 + 9
(−9+0)+9\left(-9 + 0\right) + 9 
=
0
00 
product
1*-9*9
1(−9)91 \left(-9\right) 9 
=
-81
−81-81 
-81
Rapid solution [src] 
x1 = -9
x1=−9x_{1} = -9
Simplify 
x2 = 9
x2=9x_{2} = 9
Simplify
Numerical answer [src] 
x1 = 9.0
x2 = -9.0
x2 = -9.0
The graph
1/3x^2-27=0 equation
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