What are the solutions to the equation ((x-2)^2)/3+(14x-5)/6 = 11/6 ?

The solutions to the equation ((x-2)^2)/3+(14x-5)/6 = 11/6 are x=1,x=-4

Find the zeros of ((x-2)^2)/3+(14x-5)/6 = 11/6

The zeros of ((x-2)^2)/3+(14x-5)/6 = 11/6 are x=1,x=-4

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\frac{( x - 2 ) ^{2}}{3} + \frac{14 x - 5}{6} = \frac{11}{6}

x = 1, x = - 4

Solution steps

\frac{( x - 2 ) ^{2}}{3} + \frac{14 x - 5}{6} = \frac{11}{6}

Find Least Common Multiplier of

3, 6 : 6

Multiply by LCM=

6

\frac{( x - 2 ) ^{2}}{3} \cdot 6 + \frac{14 x - 5}{6} \cdot 6 = \frac{11}{6} \cdot 6

Simplify

2 (x - 2)^{2} + 14 x - 5 = 11

Expand

2 (x - 2)^{2} + 14 x - 5 : 2 x^{2} + 6 x + 3

2 x^{2} + 6 x + 3 = 11

Move

11

to the left side

2 x^{2} + 6 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 2 ( - 8 )}{2 \cdot 2}

6^{2} - 4 \cdot 2 (- 8) = 10

x_{1, 2} = \frac{- 6 \pm 10}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 6 + 10}{2 \cdot 2}, x_{2} = \frac{- 6 - 10}{2 \cdot 2}

x = \frac{- 6 + 10}{2 \cdot 2} : 1

x = \frac{- 6 - 10}{2 \cdot 2} : - 4

The solutions to the quadratic equation are:

x = 1, x = - 4

- 0.2 x^{2} + 6 x + 10 = 0

3 x (x + 3) = 8

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

2 n^{2} + n - 2035 = 0

x, 4 x^{2} + y^{2} - 4 z^{2} - 4 = 0

What are the solutions to the equation ((x-2)^2)/3+(14x-5)/6 = 11/6 ?
The solutions to the equation ((x-2)^2)/3+(14x-5)/6 = 11/6 are x=1,x=-4
Find the zeros of ((x-2)^2)/3+(14x-5)/6 = 11/6
The zeros of ((x-2)^2)/3+(14x-5)/6 = 11/6 are x=1,x=-4