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3*x^2-6=0

3*x^2-6=0 equation

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Numerical solution:

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The solution

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   2        
3*x  - 6 = 0
3x2−6=03 x^{2} - 6 = 0
Simplify
Detail solution
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=3a = 3
b=0b = 0
c=−6c = -6
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (3) * (-6) = 72

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} = \sqrt{2}
x2=−2x_{2} = - \sqrt{2}
Vieta's Theorem
rewrite the equation
3x2−6=03 x^{2} - 6 = 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
x2−2=0x^{2} - 2 = 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=−2q = -2
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−2x_{1} x_{2} = -2
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
        ___
x1 = -\/ 2
x1=−2x_{1} = - \sqrt{2} 
       ___
x2 = \/ 2
x2=2x_{2} = \sqrt{2} 
x2 = sqrt(2)
Sum and product of roots [src] 
sum
    ___     ___
- \/ 2  + \/ 2
−2+2- \sqrt{2} + \sqrt{2} 
=
0
00 
product
   ___   ___
-\/ 2 *\/ 2
−22- \sqrt{2} \sqrt{2} 
=
-2
−2-2 
-2
Numerical answer [src] 
x1 = 1.4142135623731
x2 = -1.4142135623731
x2 = -1.4142135623731
The graph
3*x^2-6=0 equation
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