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x^2+4=5x

x^2+4=5x equation

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Numerical solution:

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The solution

You have entered [src] 
 2          
x  + 4 = 5*x
x2+4=5xx^{2} + 4 = 5 x
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2+4=5xx^{2} + 4 = 5 x
to
−5x+(x2+4)=0- 5 x + \left(x^{2} + 4\right) = 0
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=−5b = -5
c=4c = 4
, then
D = b^2 - 4 * a * c = 

(-5)^2 - 4 * (1) * (4) = 9

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

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

or
x1=4x_{1} = 4
x2=1x_{2} = 1
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−5p = -5
q=caq = \frac{c}{a}
q=4q = 4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=5x_{1} + x_{2} = 5
x1x2=4x_{1} x_{2} = 4
The graph
02468-8-6-4-2141012-250250
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 4
x2=4x_{2} = 4 
x2 = 4
Sum and product of roots [src] 
sum
1 + 4
1+41 + 4 
=
5
55 
product
4
44 
=
4
44 
4
Numerical answer [src] 
x1 = 1.0
x2 = 4.0
x2 = 4.0
The graph
x^2+4=5x equation
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