Solve 2-(x-2/3) x/4

Question

Simplify the expression

\frac{24 - 3 x ^{2} + 2 x}{12}

Show Solution

x_{1} = \frac{1 - 73}{3}, x_{2} = \frac{1 + 73}{3}

Alternative Form

x_{1} \approx - 2.514668, x_{2} \approx 3.181335

Evaluate

2 - (x - \frac{2}{3}) \times \frac{x}{4}

To find the roots of the expression,set the expression equal to 0

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

Multiply the terms

More Steps

2 - \frac{x ( 3 x - 2 )}{12} = 0

Subtract the terms

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\frac{24 - 3 x ^{2} + 2 x}{12} = 0

Simplify

24 - 3 x^{2} + 2 x = 0

Rewrite in standard form

- 3 x^{2} + 2 x + 24 = 0

Multiply both sides

3 x^{2} - 2 x - 24 = 0

Substitute a= 3,b= - 2 and c= - 24 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 3 ( - 24 )}{2 \times 3}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 3 ( - 24 )}{6}

Simplify the expression

More Steps

x = \frac{2 \pm 292}{6}

Simplify the radical expression

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x = \frac{2 \pm 2 73}{6}

Separate the equation into 2 possible cases

x = \frac{2 + 2 73}{6} x = \frac{2 - 2 73}{6}

Simplify the expression

More Steps

x = \frac{1 + 73}{3} x = \frac{2 - 2 73}{6}

Simplify the expression

More Steps

x = \frac{1 + 73}{3} x = \frac{1 - 73}{3}

Solution

x_{1} = \frac{1 - 73}{3}, x_{2} = \frac{1 + 73}{3}

Alternative Form

x_{1} \approx - 2.514668, x_{2} \approx 3.181335

Show Solution