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3a^2-21=0 equation

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Numerical solution:

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The solution

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   2         
3*a  - 21 = 0
3a2−21=03 a^{2} - 21 = 0
Simplify
Detail solution
This equation is of the form
a*a^2 + b*a + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
a1=D−b2aa_{1} = \frac{\sqrt{D} - b}{2 a}
a2=−D−b2aa_{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=−21c = -21
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (3) * (-21) = 252

Because D > 0, then the equation has two roots.
a1 = (-b + sqrt(D)) / (2*a)

a2 = (-b - sqrt(D)) / (2*a)

or
a1=7a_{1} = \sqrt{7}
a2=−7a_{2} = - \sqrt{7}
Vieta's Theorem
rewrite the equation
3a2−21=03 a^{2} - 21 = 0
of
a3+ab+c=0a^{3} + a b + c = 0
as reduced quadratic equation
a2+b+ca=0a^{2} + b + \frac{c}{a} = 0
a2−7=0a^{2} - 7 = 0
a2+ap+q=0a^{2} + a p + q = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−7q = -7
Vieta Formulas
a1+a2=−pa_{1} + a_{2} = - p
a1a2=qa_{1} a_{2} = q
a1+a2=0a_{1} + a_{2} = 0
a1a2=−7a_{1} a_{2} = -7
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
        ___
a1 = -\/ 7
a1=−7a_{1} = - \sqrt{7} 
       ___
a2 = \/ 7
a2=7a_{2} = \sqrt{7} 
a2 = sqrt(7)
Sum and product of roots [src] 
sum
    ___     ___
- \/ 7  + \/ 7
−7+7- \sqrt{7} + \sqrt{7} 
=
0
00 
product
   ___   ___
-\/ 7 *\/ 7
−77- \sqrt{7} \sqrt{7} 
=
-7
−7-7 
-7
Numerical answer [src] 
a1 = 2.64575131106459
a2 = -2.64575131106459
a2 = -2.64575131106459
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