What are the solutions to the equation 1/2 x^2-3/2 x-4/3 =0 ?

The solutions to the equation 1/2 x^2-3/2 x-4/3 =0 are x=(9+sqrt(177))/6 ,x=(9-sqrt(177))/6

Find the zeros of 1/2 x^2-3/2 x-4/3 =0

The zeros of 1/2 x^2-3/2 x-4/3 =0 are x=(9+sqrt(177))/6 ,x=(9-sqrt(177))/6

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\frac{1}{2} x^{2} - \frac{3}{2} x - \frac{4}{3} = 0

x = \frac{9 + 177}{6}, x = \frac{9 - 177}{6}

Decimal Notation

x = 3.71735 \dots, x = - 0.71735 \dots

Solution steps

\frac{1}{2} x^{2} - \frac{3}{2} x - \frac{4}{3} = 0

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{1}{2} x^{2} \cdot 6 - \frac{3}{2} x \cdot 6 - \frac{4}{3} \cdot 6 = 0 \cdot 6

Simplify

3 x^{2} - 9 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 3 ( - 8 )}{2 \cdot 3}

(- 9)^{2} - 4 \cdot 3 (- 8) = 177

x_{1, 2} = \frac{- ( - 9 ) \pm 177}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 9 ) + 177}{2 \cdot 3}, x_{2} = \frac{- ( - 9 ) - 177}{2 \cdot 3}

x = \frac{- ( - 9 ) + 177}{2 \cdot 3} : \frac{9 + 177}{6}

x = \frac{- ( - 9 ) - 177}{2 \cdot 3} : \frac{9 - 177}{6}

The solutions to the quadratic equation are:

x = \frac{9 + 177}{6}, x = \frac{9 - 177}{6}

z^{2} + 13 z + 12

\frac{1}{2} \cdot \frac{2}{2}

- 3 x - 10 < 6

x^{2} - 11 x

- 6 \geq 2 x^{2} + 8 x

What are the solutions to the equation 1/2 x^2-3/2 x-4/3 =0 ?
The solutions to the equation 1/2 x^2-3/2 x-4/3 =0 are x=(9+sqrt(177))/6 ,x=(9-sqrt(177))/6
Find the zeros of 1/2 x^2-3/2 x-4/3 =0
The zeros of 1/2 x^2-3/2 x-4/3 =0 are x=(9+sqrt(177))/6 ,x=(9-sqrt(177))/6