What are the solutions to the equation x^2+2/3 x= 7/12 ?

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

Find the zeros of x^2+2/3 x= 7/12

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

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x^{2} + \frac{2}{3} x = \frac{7}{12}

x = \frac{1}{2}, x = - \frac{7}{6}

Decimal Notation

x = 0.5, x = - 1.16666 \dots

Solution steps

x^{2} + \frac{2}{3} x = \frac{7}{12}

Find Least Common Multiplier of

3, 12 : 12

Multiply by LCM=

12

x^{2} \cdot 12 + \frac{2}{3} x \cdot 12 = \frac{7}{12} \cdot 12

Simplify

12 x^{2} + 8 x = 7

Move

7

to the left side

12 x^{2} + 8 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 12 ( - 7 )}{2 \cdot 12}

8^{2} - 4 \cdot 12 (- 7) = 20

x_{1, 2} = \frac{- 8 \pm 20}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- 8 + 20}{2 \cdot 12}, x_{2} = \frac{- 8 - 20}{2 \cdot 12}

x = \frac{- 8 + 20}{2 \cdot 12} : \frac{1}{2}

x = \frac{- 8 - 20}{2 \cdot 12} : - \frac{7}{6}

The solutions to the quadratic equation are:

x = \frac{1}{2}, x = - \frac{7}{6}

- 2 y^{2} + 32 = 0

7 x^{2} = 14 x

x^{2} + 30 x = 24150

(44 - x)^{2} = (20 - x)^{2} + (41 - x)^{2}

4 w^{2} - 12 w = 0

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