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x^2-8x+15=0

x^2-8x+15=0 equation

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Numerical solution:

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The solution

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x  - 8*x + 15 = 0
(x2−8x)+15=0\left(x^{2} - 8 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=1a = 1
b=−8b = -8
c=15c = 15
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (1) * (15) = 4

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

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

or
x1=5x_{1} = 5
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=−8p = -8
q=caq = \frac{c}{a}
q=15q = 15
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=8x_{1} + x_{2} = 8
x1x2=15x_{1} x_{2} = 15
The graph
05-10-5101520200-100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 3
x1=3x_{1} = 3 
x2 = 5
x2=5x_{2} = 5 
x2 = 5
Sum and product of roots [src] 
sum
3 + 5
3+53 + 5 
=
8
88 
product
3*5
3⋅53 \cdot 5 
=
15
1515 
15
Numerical answer [src] 
x1 = 5.0
x2 = 3.0
x2 = 3.0
The graph
x^2-8x+15=0 equation
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