What are the solutions to the equation x((3x+1)/2)=6 ?

The solutions to the equation x((3x+1)/2)=6 are x=(-1+sqrt(145))/6 ,x=(-1-sqrt(145))/6

Find the zeros of x((3x+1)/2)=6

The zeros of x((3x+1)/2)=6 are x=(-1+sqrt(145))/6 ,x=(-1-sqrt(145))/6

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x (\frac{3 x + 1}{2}) = 6

x = \frac{- 1 + 145}{6}, x = \frac{- 1 - 145}{6}

Decimal Notation

x = 1.84026 \dots, x = - 2.17359 \dots

Solution steps

x (\frac{3 x + 1}{2}) = 6

Expand

x (\frac{3 x + 1}{2}) : \frac{3 x ^{2}}{2} + \frac{x}{2}

\frac{3 x ^{2}}{2} + \frac{x}{2} = 6

Move

6

to the left side

\frac{3 x ^{2} + x}{2} - 6 = 0

Write in the standard form

a x^{2} + b x + c = 0

\frac{3 x ^{2}}{2} + \frac{1 \cdot x}{2} - 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- \frac{1}{2} \pm ( \frac{1}{2} ) ^{2} - 4 \cdot \frac{3}{2} ( - 6 )}{2 \cdot \frac{3}{2}}

(\frac{1}{2})^{2} - 4 \cdot \frac{3}{2} (- 6) = \frac{145}{2}

x_{1, 2} = \frac{- \frac{1}{2} \pm \frac{145}{2}}{2 \cdot \frac{3}{2}}

Separate the solutions

x_{1} = \frac{- \frac{1}{2} + \frac{145}{2}}{2 \cdot \frac{3}{2}}, x_{2} = \frac{- \frac{1}{2} - \frac{145}{2}}{2 \cdot \frac{3}{2}}

x = \frac{- \frac{1}{2} + \frac{145}{2}}{2 \frac{3}{2}} : \frac{- 1 + 145}{6}

x = \frac{- \frac{1}{2} - \frac{145}{2}}{2 \frac{3}{2}} : \frac{- 1 - 145}{6}

The solutions to the quadratic equation are:

x = \frac{- 1 + 145}{6}, x = \frac{- 1 - 145}{6}

a = x^{2} - 4 x + 1

e = m^{0} \frac{c ^{2}}{1} - \frac{v ^{2}}{c ^{2}}

(t) = - t^{2} + 22 t - 85

x, a = (x - 5)^{2} + 5 y^{6} - 30

\frac{2 x ^{2}}{3} = 32

What are the solutions to the equation x((3x+1)/2)=6 ?
The solutions to the equation x((3x+1)/2)=6 are x=(-1+sqrt(145))/6 ,x=(-1-sqrt(145))/6
Find the zeros of x((3x+1)/2)=6
The zeros of x((3x+1)/2)=6 are x=(-1+sqrt(145))/6 ,x=(-1-sqrt(145))/6