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2x^2−14x+12=0 equation

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Numerical solution:

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The solution

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2*x  - 14*x + 12 = 0
(2x2−14x)+12=0\left(2 x^{2} - 14 x\right) + 12 = 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=2a = 2
b=−14b = -14
c=12c = 12
, then
D = b^2 - 4 * a * c = 

(-14)^2 - 4 * (2) * (12) = 100

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=6x_{1} = 6
x2=1x_{2} = 1
Vieta's Theorem
rewrite the equation
(2x2−14x)+12=0\left(2 x^{2} - 14 x\right) + 12 = 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
x2−7x+6=0x^{2} - 7 x + 6 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−7p = -7
q=caq = \frac{c}{a}
q=6q = 6
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=7x_{1} + x_{2} = 7
x1x2=6x_{1} x_{2} = 6
The graph
05-10-5101520-500500
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
1 + 6
1+61 + 6 
=
7
77 
product
6
66 
=
6
66 
6
Rapid solution [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 6
x2=6x_{2} = 6 
x2 = 6
Numerical answer [src] 
x1 = 1.0
x2 = 6.0
x2 = 6.0
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