Solve (3x - 48)/(2x + 48)=3x - 4x

Question

Solve the equation

x_{1} = - \frac{51 + 2985}{4}, x_{2} = \frac{- 51 + 2985}{4}

Alternative Form

x_{1} \approx - 26.408788, x_{2} \approx 0.908788

Evaluate

\frac{3 x - 48}{2 x + 48} = 3 x - 4 x

Find the domain

More Steps

\frac{3 x - 48}{2 x + 48} = 3 x - 4 x, x \neq = - 24

Subtract the terms

More Steps

\frac{3 x - 48}{2 x + 48} = - x

Cross multiply

3 x - 48 = (2 x + 48) (- x)

Simplify the equation

3 x - 48 = - x (2 x + 48)

Expand the expression

More Steps

3 x - 48 = - 2 x^{2} - 48 x

Move the expression to the left side

3 x - 48 - (- 2 x^{2} - 48 x) = 0

Subtract the terms

More Steps

51 x - 48 + 2 x^{2} = 0

Rewrite in standard form

2 x^{2} + 51 x - 48 = 0

Substitute a= 2,b= 51 and c= - 48 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 51 \pm 5 1 ^{2} - 4 \times 2 ( - 48 )}{2 \times 2}

Simplify the expression

x = \frac{- 51 \pm 5 1 ^{2} - 4 \times 2 ( - 48 )}{4}

Simplify the expression

More Steps

x = \frac{- 51 \pm 2985}{4}

Separate the equation into 2 possible cases

x = \frac{- 51 + 2985}{4} x = \frac{- 51 - 2985}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = \frac{- 51 + 2985}{4} x = - \frac{51 + 2985}{4}

Check if the solution is in the defined range

x = \frac{- 51 + 2985}{4} x = - \frac{51 + 2985}{4}, x \neq = - 24

Find the intersection of the solution and the defined range

x = \frac{- 51 + 2985}{4} x = - \frac{51 + 2985}{4}

Solution

x_{1} = - \frac{51 + 2985}{4}, x_{2} = \frac{- 51 + 2985}{4}

Alternative Form

x_{1} \approx - 26.408788, x_{2} \approx 0.908788

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