Solve (2x - 7)/42x - (4x - 9)/3 = x/2

Question

Solve the equation

x_{1} = 21 - 342, x_{2} = 21 + 342

Alternative Form

x_{1} \approx 1.557778, x_{2} \approx 40.442222

Evaluate

\frac{2 x - 7}{42} \times x - \frac{4 x - 9}{3} = \frac{x}{2}

Multiply the terms

More Steps

\frac{x ( 2 x - 7 )}{42} - \frac{4 x - 9}{3} = \frac{x}{2}

Multiply both sides of the equation by LCD

(\frac{x ( 2 x - 7 )}{42} - \frac{4 x - 9}{3}) \times 42 = \frac{x}{2} \times 42

Simplify the equation

More Steps

2 x^{2} - 63 x + 126 = \frac{x}{2} \times 42

Simplify the equation

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2 x^{2} - 63 x + 126 = 21 x

Move the expression to the left side

2 x^{2} - 63 x + 126 - 21 x = 0

Subtract the terms

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2 x^{2} - 84 x + 126 = 0

Substitute a= 2,b= - 84 and c= 126 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{84 \pm ( - 84 ) ^{2} - 4 \times 2 \times 126}{2 \times 2}

Simplify the expression

x = \frac{84 \pm ( - 84 ) ^{2} - 4 \times 2 \times 126}{4}

Simplify the expression

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x = \frac{84 \pm 6048}{4}

Simplify the radical expression

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x = \frac{84 \pm 12 42}{4}

Separate the equation into 2 possible cases

x = \frac{84 + 12 42}{4} x = \frac{84 - 12 42}{4}

Simplify the expression

More Steps

x = 21 + 342 x = \frac{84 - 12 42}{4}

Simplify the expression

More Steps

x = 21 + 342 x = 21 - 342

Solution

x_{1} = 21 - 342, x_{2} = 21 + 342

Alternative Form

x_{1} \approx 1.557778, x_{2} \approx 40.442222

Show Solution