What are the solutions to the equation x^2-7/6 x+1/3 =6 ?

The solutions to the equation x^2-7/6 x+1/3 =6 are x=(7+sqrt(865))/(12),x=(7-sqrt(865))/(12)

Find the zeros of x^2-7/6 x+1/3 =6

The zeros of x^2-7/6 x+1/3 =6 are x=(7+sqrt(865))/(12),x=(7-sqrt(865))/(12)

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x^{2} - \frac{7}{6} x + \frac{1}{3} = 6

x = \frac{7 + 865}{12}, x = \frac{7 - 865}{12}

Decimal Notation

x = 3.03424 \dots, x = - 1.86757 \dots

Solution steps

x^{2} - \frac{7}{6} x + \frac{1}{3} = 6

Find Least Common Multiplier of

6, 3 : 6

Multiply by LCM=

6

x^{2} \cdot 6 - \frac{7}{6} x \cdot 6 + \frac{1}{3} \cdot 6 = 6 \cdot 6

Simplify

6 x^{2} - 7 x + 2 = 36

Move

36

to the left side

6 x^{2} - 7 x - 34 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 6 ( - 34 )}{2 \cdot 6}

(- 7)^{2} - 4 \cdot 6 (- 34) = 865

x_{1, 2} = \frac{- ( - 7 ) \pm 865}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 865}{2 \cdot 6}, x_{2} = \frac{- ( - 7 ) - 865}{2 \cdot 6}

x = \frac{- ( - 7 ) + 865}{2 \cdot 6} : \frac{7 + 865}{12}

x = \frac{- ( - 7 ) - 865}{2 \cdot 6} : \frac{7 - 865}{12}

The solutions to the quadratic equation are:

x = \frac{7 + 865}{12}, x = \frac{7 - 865}{12}

(x + 5) (x - 3) = 20

7^{2} = 5^{2} + x^{2}

- 3 x^{2} - 5 x - 6 = 0

3^{2} + 1^{2} = c^{2}

d^{2} - 3 d = 0

What are the solutions to the equation x^2-7/6 x+1/3 =6 ?
The solutions to the equation x^2-7/6 x+1/3 =6 are x=(7+sqrt(865))/(12),x=(7-sqrt(865))/(12)
Find the zeros of x^2-7/6 x+1/3 =6
The zeros of x^2-7/6 x+1/3 =6 are x=(7+sqrt(865))/(12),x=(7-sqrt(865))/(12)