Solve (x-3)/4 (x-1)/5 = (x-2)/3 - 1

Question

Solve the equation

x \in / R

Alternative Form

No real solution

Evaluate

\frac{x - 3}{4} \times \frac{x - 1}{5} = \frac{x - 2}{3} - 1

Multiply the terms

More Steps

\frac{( x - 3 ) ( x - 1 )}{20} = \frac{x - 2}{3} - 1

Multiply both sides of the equation by LCD

\frac{( x - 3 ) ( x - 1 )}{20} \times 60 = (\frac{x - 2}{3} - 1) \times 60

Simplify the equation

More Steps

3 x^{2} - 12 x + 9 = (\frac{x - 2}{3} - 1) \times 60

Simplify the equation

More Steps

3 x^{2} - 12 x + 9 = 20 x - 100

Move the expression to the left side

3 x^{2} - 12 x + 9 - (20 x - 100) = 0

Calculate the sum or difference

More Steps

3 x^{2} - 32 x + 109 = 0

Substitute a= 3,b= - 32 and c= 109 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{32 \pm ( - 32 ) ^{2} - 4 \times 3 \times 109}{2 \times 3}

Simplify the expression

x = \frac{32 \pm ( - 32 ) ^{2} - 4 \times 3 \times 109}{6}

Simplify the expression

More Steps

x = \frac{32 \pm - 284}{6}

Solution

x \in / R

Alternative Form

No real solution

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