Solve x^2 5/12 = 2-8x/3

Question

Solve the equation

x_{1} = - \frac{16 + 2 94}{5}, x_{2} = \frac{- 16 + 2 94}{5}

Alternative Form

x_{1} \approx - 7.078144, x_{2} \approx 0.678144

Evaluate

x^{2} \times \frac{5}{12} = 2 - (8 \times \frac{x}{3})

Use the commutative property to reorder the terms

\frac{5}{12} x^{2} = 2 - (8 \times \frac{x}{3})

Multiply the terms

\frac{5}{12} x^{2} = 2 - \frac{8 x}{3}

Multiply both sides of the equation by LCD

\frac{5}{12} x^{2} \times 12 = (2 - \frac{8 x}{3}) \times 12

Simplify the equation

5 x^{2} = (2 - \frac{8 x}{3}) \times 12

Simplify the equation

More Steps

5 x^{2} = 24 - 32 x

Move the expression to the left side

5 x^{2} - (24 - 32 x) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

5 x^{2} - 24 + 32 x = 0

Rewrite in standard form

5 x^{2} + 32 x - 24 = 0

Substitute a= 5,b= 32 and c= - 24 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 32 \pm 3 2 ^{2} - 4 \times 5 ( - 24 )}{2 \times 5}

Simplify the expression

x = \frac{- 32 \pm 3 2 ^{2} - 4 \times 5 ( - 24 )}{10}

Simplify the expression

More Steps

x = \frac{- 32 \pm 1504}{10}

Simplify the radical expression

More Steps

x = \frac{- 32 \pm 4 94}{10}

Separate the equation into 2 possible cases

x = \frac{- 32 + 4 94}{10} x = \frac{- 32 - 4 94}{10}

Simplify the expression

More Steps

x = \frac{- 16 + 2 94}{5} x = \frac{- 32 - 4 94}{10}

Simplify the expression

More Steps

x = \frac{- 16 + 2 94}{5} x = - \frac{16 + 2 94}{5}

Solution

x_{1} = - \frac{16 + 2 94}{5}, x_{2} = \frac{- 16 + 2 94}{5}

Alternative Form

x_{1} \approx - 7.078144, x_{2} \approx 0.678144

Show Solution

Solve the equation

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