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9+12x-5x^2=0

9+12x-5x^2=0 equation

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Numerical solution:

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The solution

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9 + 12*x - 5*x  = 0
−5x2+(12x+9)=0- 5 x^{2} + \left(12 x + 9\right) = 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=−5a = -5
b=12b = 12
c=9c = 9
, then
D = b^2 - 4 * a * c = 

(12)^2 - 4 * (-5) * (9) = 324

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

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

or
x1=−35x_{1} = - \frac{3}{5}
x2=3x_{2} = 3
Vieta's Theorem
rewrite the equation
−5x2+(12x+9)=0- 5 x^{2} + \left(12 x + 9\right) = 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
x2−12x5−95=0x^{2} - \frac{12 x}{5} - \frac{9}{5} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−125p = - \frac{12}{5}
q=caq = \frac{c}{a}
q=−95q = - \frac{9}{5}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=125x_{1} + x_{2} = \frac{12}{5}
x1x2=−95x_{1} x_{2} = - \frac{9}{5}
The graph
05-15-10-51015-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
3 - 3/5
−35+3- \frac{3}{5} + 3 
=
12/5
125\frac{12}{5} 
product
3*(-3)
------
  5
(−3)35\frac{\left(-3\right) 3}{5} 
=
-9/5
−95- \frac{9}{5} 
-9/5
Rapid solution [src] 
x1 = -3/5
x1=−35x_{1} = - \frac{3}{5} 
x2 = 3
x2=3x_{2} = 3 
x2 = 3
Numerical answer [src] 
x1 = -0.6
x2 = 3.0
x2 = 3.0
The graph
9+12x-5x^2=0 equation
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