Solve 4-2x/3=x^2/3 - ScanMath

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Question

Solve the equation

x_{1} = - 1 - 13, x_{2} = - 1 + 13

Alternative Form

x_{1} \approx - 4.605551, x_{2} \approx 2.605551

Evaluate

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

Multiply the terms

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

Multiply both sides of the equation by LCD

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

Simplify the equation

More Steps

12 - 2 x = \frac{x ^{2}}{3} \times 3

Simplify the equation

12 - 2 x = x^{2}

Move the expression to the left side

12 - 2 x - x^{2} = 0

Rewrite in standard form

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

Multiply both sides

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

Substitute a= 1,b= 2 and c= - 12 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 2 \pm 2 ^{2} - 4 ( - 12 )}{2}

Simplify the expression

More Steps

x = \frac{- 2 \pm 52}{2}

Simplify the radical expression

More Steps

x = \frac{- 2 \pm 2 13}{2}

Separate the equation into 2 possible cases

x = \frac{- 2 + 2 13}{2} x = \frac{- 2 - 2 13}{2}

Simplify the expression

More Steps

x = - 1 + 13 x = \frac{- 2 - 2 13}{2}

Simplify the expression

More Steps

x = - 1 + 13 x = - 1 - 13

Solution

x_{1} = - 1 - 13, x_{2} = - 1 + 13

Alternative Form

x_{1} \approx - 4.605551, x_{2} \approx 2.605551

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