What are the solutions to the equation (2x^2)/4-x/6 = 3/2 ?

The solutions to the equation (2x^2)/4-x/6 = 3/2 are x=(1+sqrt(109))/6 ,x=(1-sqrt(109))/6

Find the zeros of (2x^2)/4-x/6 = 3/2

The zeros of (2x^2)/4-x/6 = 3/2 are x=(1+sqrt(109))/6 ,x=(1-sqrt(109))/6

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\frac{2 x ^{2}}{4} - \frac{x}{6} = \frac{3}{2}

x = \frac{1 + 109}{6}, x = \frac{1 - 109}{6}

Decimal Notation

x = 1.90671 \dots, x = - 1.57338 \dots

Solution steps

\frac{2 x ^{2}}{4} - \frac{x}{6} = \frac{3}{2}

Find Least Common Multiplier of

4, 6, 2 : 12

Multiply by LCM=

12

\frac{2 x ^{2}}{4} \cdot 12 - \frac{x}{6} \cdot 12 = \frac{3}{2} \cdot 12

Simplify

6 x^{2} - 2 x = 18

Move

18

to the left side

6 x^{2} - 2 x - 18 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 6 ( - 18 )}{2 \cdot 6}

(- 2)^{2} - 4 \cdot 6 (- 18) = 2109

x_{1, 2} = \frac{- ( - 2 ) \pm 2 109}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 109}{2 \cdot 6}, x_{2} = \frac{- ( - 2 ) - 2 109}{2 \cdot 6}

x = \frac{- ( - 2 ) + 2 109}{2 \cdot 6} : \frac{1 + 109}{6}

x = \frac{- ( - 2 ) - 2 109}{2 \cdot 6} : \frac{1 - 109}{6}

The solutions to the quadratic equation are:

x = \frac{1 + 109}{6}, x = \frac{1 - 109}{6}

12 x^{2} - 108 x = 0

\frac{5 x}{2} = \frac{5 x ^{2}}{4}

x, x^{2} y = x - 3

2 x^{2} + 31 = 17

5 (x + 5)^{2} - 33 = 2

What are the solutions to the equation (2x^2)/4-x/6 = 3/2 ?
The solutions to the equation (2x^2)/4-x/6 = 3/2 are x=(1+sqrt(109))/6 ,x=(1-sqrt(109))/6
Find the zeros of (2x^2)/4-x/6 = 3/2
The zeros of (2x^2)/4-x/6 = 3/2 are x=(1+sqrt(109))/6 ,x=(1-sqrt(109))/6