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3x^2+7x-6=0

3x^2+7x-6=0 equation

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Numerical solution:

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The solution

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3*x  + 7*x - 6 = 0
(3x2+7x)−6=0\left(3 x^{2} + 7 x\right) - 6 = 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=7b = 7
c=−6c = -6
, then
D = b^2 - 4 * a * c = 

(7)^2 - 4 * (3) * (-6) = 121

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

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

or
x1=23x_{1} = \frac{2}{3}
x2=−3x_{2} = -3
Vieta's Theorem
rewrite the equation
(3x2+7x)−6=0\left(3 x^{2} + 7 x\right) - 6 = 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+7x3−2=0x^{2} + \frac{7 x}{3} - 2 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=73p = \frac{7}{3}
q=caq = \frac{c}{a}
q=−2q = -2
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−73x_{1} + x_{2} = - \frac{7}{3}
x1x2=−2x_{1} x_{2} = -2
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -3
x1=−3x_{1} = -3 
x2 = 2/3
x2=23x_{2} = \frac{2}{3} 
x2 = 2/3
Sum and product of roots [src] 
sum
-3 + 2/3
−3+23-3 + \frac{2}{3} 
=
-7/3
−73- \frac{7}{3} 
product
-3*2
----
 3
−2- 2 
=
-2
−2-2 
-2
Numerical answer [src] 
x1 = -3.0
x2 = 0.666666666666667
x2 = 0.666666666666667
The graph
3x^2+7x-6=0 equation
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