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

The solutions to the equation (x^2-x)/2-((x-4)^2)/3 =0 are x=(-13+3sqrt(33))/2 ,x=(-13-3sqrt(33))/2

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

The zeros of (x^2-x)/2-((x-4)^2)/3 =0 are x=(-13+3sqrt(33))/2 ,x=(-13-3sqrt(33))/2

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

x = \frac{- 13 + 3 33}{2}, x = \frac{- 13 - 3 33}{2}

Decimal Notation

x = 2.11684 \dots, x = - 15.11684 \dots

Solution steps

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

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

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

Simplify

3 (x^{2} - x) - 2 (x - 4)^{2} = 0

Expand

3 (x^{2} - x) - 2 (x - 4)^{2} : x^{2} + 13 x - 32

x^{2} + 13 x - 32 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 13 \pm 1 3 ^{2} - 4 \cdot 1 \cdot ( - 32 )}{2 \cdot 1}

1 3^{2} - 4 \cdot 1 \cdot (- 32) = 333

x_{1, 2} = \frac{- 13 \pm 3 33}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 13 + 3 33}{2 \cdot 1}, x_{2} = \frac{- 13 - 3 33}{2 \cdot 1}

x = \frac{- 13 + 3 33}{2 \cdot 1} : \frac{- 13 + 3 33}{2}

x = \frac{- 13 - 3 33}{2 \cdot 1} : \frac{- 13 - 3 33}{2}

The solutions to the quadratic equation are:

x = \frac{- 13 + 3 33}{2}, x = \frac{- 13 - 3 33}{2}

- 0.45 x^{2} + 5.52 x - 13.7 = 0

x, z = 4 (x - y) - x^{2} - y^{2}

20 x^{2} - 27 x - 14 = 0

4 y^{2} + 20 y = 0

x^{2} + 8.9 x + 18.7 = 0

What are the solutions to the equation (x^2-x)/2-((x-4)^2)/3 =0 ?
The solutions to the equation (x^2-x)/2-((x-4)^2)/3 =0 are x=(-13+3sqrt(33))/2 ,x=(-13-3sqrt(33))/2
Find the zeros of (x^2-x)/2-((x-4)^2)/3 =0
The zeros of (x^2-x)/2-((x-4)^2)/3 =0 are x=(-13+3sqrt(33))/2 ,x=(-13-3sqrt(33))/2