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7x^2-21=0

7x^2-21=0 equation

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Numerical solution:

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The solution

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7*x  - 21 = 0
7x2−21=07 x^{2} - 21 = 0
Simplify
Detail solution
This equation is of the form
a x2+b x+c=0a\ 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=b2−4acD = b^2 - 4 a c is the discriminant.
Because
a=7a = 7
b=0b = 0
c=−21c = -21
, then
D=b2−4 a c=D = b^2 - 4\ a\ c =
02−7⋅4(−21)=5880^{2} - 7 \cdot 4 \left(-21\right) = 588
Because D > 0, then the equation has two roots.
x1=(−b+D)2ax_1 = \frac{(-b + \sqrt{D})}{2 a}
x2=(−b−D)2ax_2 = \frac{(-b - \sqrt{D})}{2 a}
or
x1=3x_{1} = \sqrt{3}
Simplify
x2=−3x_{2} = - \sqrt{3}
Simplify
Vieta's Theorem
rewrite the equation
7x2−21=07 x^{2} - 21 = 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
x2−3=0x^{2} - 3 = 0
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−3q = -3
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−3x_{1} x_{2} = -3
The graph
05-15-10-51015-100100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
   ___     ___
-\/ 3  + \/ 3
(−3)+(3)\left(- \sqrt{3}\right) + \left(\sqrt{3}\right) 
=
0
00
Simplify 
product
   ___     ___
-\/ 3  * \/ 3
(−3)∗(3)\left(- \sqrt{3}\right) * \left(\sqrt{3}\right) 
=
-3
−3-3
Simplify
Rapid solution [src] 
         ___
x_1 = -\/ 3
x1=−3x_{1} = - \sqrt{3}
Simplify 
        ___
x_2 = \/ 3
x2=3x_{2} = \sqrt{3}
Simplify
Numerical answer [src] 
x1 = 1.73205080756888
x2 = -1.73205080756888
x2 = -1.73205080756888
The graph
7x^2-21=0 equation
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