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5/4x^2+7x+9=0

5/4x^2+7x+9=0 equation

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Numerical solution:

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The solution

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   2              
5*x               
---- + 7*x + 9 = 0
 4
(5x24+7x)+9=0\left(\frac{5 x^{2}}{4} + 7 x\right) + 9 = 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=54a = \frac{5}{4}
b=7b = 7
c=9c = 9
, then
D = b^2 - 4 * a * c = 

(7)^2 - 4 * (5/4) * (9) = 4

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

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

or
x1=−2x_{1} = -2
x2=−185x_{2} = - \frac{18}{5}
Vieta's Theorem
rewrite the equation
(5x24+7x)+9=0\left(\frac{5 x^{2}}{4} + 7 x\right) + 9 = 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+28x5+365=0x^{2} + \frac{28 x}{5} + \frac{36}{5} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=285p = \frac{28}{5}
q=caq = \frac{c}{a}
q=365q = \frac{36}{5}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−285x_{1} + x_{2} = - \frac{28}{5}
x1x2=365x_{1} x_{2} = \frac{36}{5}
The graph
05-20-15-10-510-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -18/5
x1=−185x_{1} = - \frac{18}{5} 
x2 = -2
x2=−2x_{2} = -2 
x2 = -2
Sum and product of roots [src] 
sum
-2 - 18/5
−185−2- \frac{18}{5} - 2 
=
-28/5
−285- \frac{28}{5} 
product
-2*(-18)
--------
   5
−−365- \frac{-36}{5} 
=
36/5
365\frac{36}{5} 
36/5
Numerical answer [src] 
x1 = -3.6
x2 = -2.0
x2 = -2.0
The graph
5/4x^2+7x+9=0 equation
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