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2x^2-9x+15=0

2x^2-9x+15=0 equation

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The solution

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   2               
2*x  - 9*x + 15 = 0
(2x2−9x)+15=0\left(2 x^{2} - 9 x\right) + 15 = 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=2a = 2
b=−9b = -9
c=15c = 15
, then
D = b^2 - 4 * a * c = 

(-9)^2 - 4 * (2) * (15) = -39

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

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

or
x1=94+39i4x_{1} = \frac{9}{4} + \frac{\sqrt{39} i}{4}
x2=94−39i4x_{2} = \frac{9}{4} - \frac{\sqrt{39} i}{4}
Vieta's Theorem
rewrite the equation
(2x2−9x)+15=0\left(2 x^{2} - 9 x\right) + 15 = 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
x2−9x2+152=0x^{2} - \frac{9 x}{2} + \frac{15}{2} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−92p = - \frac{9}{2}
q=caq = \frac{c}{a}
q=152q = \frac{15}{2}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=92x_{1} + x_{2} = \frac{9}{2}
x1x2=152x_{1} x_{2} = \frac{15}{2}
The graph
-0.50.00.51.01.52.02.53.03.54.04.55.05.56.06.57.0020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
        ____           ____
9   I*\/ 39    9   I*\/ 39 
- - -------- + - + --------
4      4       4      4
(94−39i4)+(94+39i4)\left(\frac{9}{4} - \frac{\sqrt{39} i}{4}\right) + \left(\frac{9}{4} + \frac{\sqrt{39} i}{4}\right) 
=
9/2
92\frac{9}{2} 
product
/        ____\ /        ____\
|9   I*\/ 39 | |9   I*\/ 39 |
|- - --------|*|- + --------|
\4      4    / \4      4    /
(94−39i4)(94+39i4)\left(\frac{9}{4} - \frac{\sqrt{39} i}{4}\right) \left(\frac{9}{4} + \frac{\sqrt{39} i}{4}\right) 
=
15/2
152\frac{15}{2} 
15/2
Rapid solution [src] 
             ____
     9   I*\/ 39 
x1 = - - --------
     4      4
x1=94−39i4x_{1} = \frac{9}{4} - \frac{\sqrt{39} i}{4} 
             ____
     9   I*\/ 39 
x2 = - + --------
     4      4
x2=94+39i4x_{2} = \frac{9}{4} + \frac{\sqrt{39} i}{4} 
x2 = 9/4 + sqrt(39)*i/4
Numerical answer [src] 
x1 = 2.25 - 1.5612494995996*i
x2 = 2.25 + 1.5612494995996*i
x2 = 2.25 + 1.5612494995996*i
The graph
2x^2-9x+15=0 equation
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