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3x^2-2x-8=0

3x^2-2x-8=0 equation

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Numerical solution:

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The solution

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   2              
3*x  - 2*x - 8 = 0
(3x2−2x)−8=0\left(3 x^{2} - 2 x\right) - 8 = 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=−2b = -2
c=−8c = -8
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (3) * (-8) = 100

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} = 2
x2=−43x_{2} = - \frac{4}{3}
Vieta's Theorem
rewrite the equation
(3x2−2x)−8=0\left(3 x^{2} - 2 x\right) - 8 = 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
x2−2x3−83=0x^{2} - \frac{2 x}{3} - \frac{8}{3} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−23p = - \frac{2}{3}
q=caq = \frac{c}{a}
q=−83q = - \frac{8}{3}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=23x_{1} + x_{2} = \frac{2}{3}
x1x2=−83x_{1} x_{2} = - \frac{8}{3}
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
2 - 4/3
−43+2- \frac{4}{3} + 2 
=
2/3
23\frac{2}{3} 
product
2*(-4)
------
  3
(−4)23\frac{\left(-4\right) 2}{3} 
=
-8/3
−83- \frac{8}{3} 
-8/3
Rapid solution [src] 
x1 = -4/3
x1=−43x_{1} = - \frac{4}{3} 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Numerical answer [src] 
x1 = -1.33333333333333
x2 = 2.0
x2 = 2.0
The graph
3x^2-2x-8=0 equation
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