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3x^2-28x+9=0 equation

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3*x  - 28*x + 9 = 0
(3x2−28x)+9=0\left(3 x^{2} - 28 x\right) + 9 = 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=−28b = -28
c=9c = 9
, then
D = b^2 - 4 * a * c = 

(-28)^2 - 4 * (3) * (9) = 676

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
x2=13x_{2} = \frac{1}{3}
Vieta's Theorem
rewrite the equation
(3x2−28x)+9=0\left(3 x^{2} - 28 x\right) + 9 = 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
x2−28x3+3=0x^{2} - \frac{28 x}{3} + 3 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−283p = - \frac{28}{3}
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=283x_{1} + x_{2} = \frac{28}{3}
x1x2=3x_{1} x_{2} = 3
Sum and product of roots [src] 
sum
9 + 1/3
13+9\frac{1}{3} + 9 
=
28/3
283\frac{28}{3} 
product
9
-
3
93\frac{9}{3} 
=
3
33 
3
Rapid solution [src] 
x1 = 1/3
x1=13x_{1} = \frac{1}{3} 
x2 = 9
x2=9x_{2} = 9 
x2 = 9
Numerical answer [src] 
x1 = 0.333333333333333
x2 = 9.0
x2 = 9.0
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