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x^2-3*x-18=0

x^2-3*x-18=0 equation

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Numerical solution:

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The solution

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 2               
x  - 3*x - 18 = 0
(x2−3x)−18=0\left(x^{2} - 3 x\right) - 18 = 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=1a = 1
b=−3b = -3
c=−18c = -18
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (-18) = 81

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=−3x_{2} = -3
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−3p = -3
q=caq = \frac{c}{a}
q=−18q = -18
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=3x_{1} + x_{2} = 3
x1x2=−18x_{1} x_{2} = -18
The graph
05-15-10-5101520-250250
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -3
x1=−3x_{1} = -3 
x2 = 6
x2=6x_{2} = 6 
x2 = 6
Sum and product of roots [src] 
sum
-3 + 6
−3+6-3 + 6 
=
3
33 
product
-3*6
−18- 18 
=
-18
−18-18 
-18
Numerical answer [src] 
x1 = 6.0
x2 = -3.0
x2 = -3.0
The graph
x^2-3*x-18=0 equation
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