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6*x^2+x-7=0

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

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Numerical solution:

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The solution

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6*x  + x - 7 = 0
$$\left(6 x^{2} + x\right) - 7 = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 6$$
$$b = 1$$
$$c = -7$$
, 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
$$x_{1} = 1$$
$$x_{2} = - \frac{7}{6}$$
Vieta's Theorem
rewrite the equation
$$\left(6 x^{2} + x\right) - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{6} - \frac{7}{6} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{6}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{6}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{6}$$
$$x_{1} x_{2} = - \frac{7}{6}$$
The graph
Sum and product of roots [src]
sum
1 - 7/6
$$- \frac{7}{6} + 1$$
=
-1/6
$$- \frac{1}{6}$$
product
-7/6
$$- \frac{7}{6}$$
=
-7/6
$$- \frac{7}{6}$$
-7/6
Rapid solution [src]
x1 = -7/6
$$x_{1} = - \frac{7}{6}$$
x2 = 1
$$x_{2} = 1$$
x2 = 1
Numerical answer [src]
x1 = 1.0
x2 = -1.16666666666667
x2 = -1.16666666666667
The graph
6*x^2+x-7=0 equation