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sqrt(3x+1)=9-x equation

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Numerical solution:

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The solution

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\/ 3*x + 1  = 9 - x
3x+1=9−x\sqrt{3 x + 1} = 9 - x
Simplify
Detail solution
Given the equation
3x+1=9−x\sqrt{3 x + 1} = 9 - x
3x+1=9−x\sqrt{3 x + 1} = 9 - x
We raise the equation sides to 2-th degree
3x+1=(9−x)23 x + 1 = \left(9 - x\right)^{2}
3x+1=x2−18x+813 x + 1 = x^{2} - 18 x + 81
Transfer the right side of the equation left part with negative sign
−x2+21x−80=0- x^{2} + 21 x - 80 = 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=21b = 21
c=−80c = -80
, then
D = b^2 - 4 * a * c = 

(21)^2 - 4 * (-1) * (-80) = 121

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=16x_{2} = 16

Because
3x+1=9−x\sqrt{3 x + 1} = 9 - x
and
3x+1≥0\sqrt{3 x + 1} \geq 0
then
9−x≥09 - x \geq 0
or
x≤9x \leq 9
−∞<x-\infty < x
The final answer:
x1=5x_{1} = 5
The graph
02468-4-2101214-2020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 5
x1=5x_{1} = 5 
x1 = 5
Sum and product of roots [src] 
sum
5
55 
=
5
55 
product
5
55 
=
5
55 
5
Numerical answer [src] 
x1 = 5.0
x1 = 5.0
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