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6*x^2+x-7=0

6*x^2+x-7=0 equation

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The solution

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6*x  + x - 7 = 0
(6x2+x)−7=0\left(6 x^{2} + x\right) - 7 = 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=6a = 6
b=1b = 1
c=−7c = -7
, then
D = b^2 - 4 * a * c = 

(1)^2 - 4 * (6) * (-7) = 169

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

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

or
x1=1x_{1} = 1
x2=−76x_{2} = - \frac{7}{6}
Vieta's Theorem
rewrite the equation
(6x2+x)−7=0\left(6 x^{2} + x\right) - 7 = 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+x6−76=0x^{2} + \frac{x}{6} - \frac{7}{6} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=16p = \frac{1}{6}
q=caq = \frac{c}{a}
q=−76q = - \frac{7}{6}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−16x_{1} + x_{2} = - \frac{1}{6}
x1x2=−76x_{1} x_{2} = - \frac{7}{6}
The graph
05-15-10-51015-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
1 - 7/6
−76+1- \frac{7}{6} + 1 
=
-1/6
−16- \frac{1}{6} 
product
-7/6
−76- \frac{7}{6} 
=
-7/6
−76- \frac{7}{6} 
-7/6
Rapid solution [src] 
x1 = -7/6
x1=−76x_{1} = - \frac{7}{6} 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Numerical answer [src] 
x1 = 1.0
x2 = -1.16666666666667
x2 = -1.16666666666667
The graph
6*x^2+x-7=0 equation
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