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

Evaluate

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

Multiply the terms

More Steps

\frac{( x - 1 ) ( x - 2 )}{6} = \frac{x - 3}{4}

Rewrite the expression

\frac{1}{6} x^{2} - \frac{1}{2} x + \frac{1}{3} = \frac{x - 3}{4}

Rewrite the expression

\frac{1}{6} x^{2} - \frac{1}{2} x + \frac{1}{3} = \frac{1}{4} x - \frac{3}{4}

Move the expression to the left side

\frac{1}{6} x^{2} - \frac{3}{4} x + \frac{13}{12} = 0

Multiply both sides

12 (\frac{1}{6} x^{2} - \frac{3}{4} x + \frac{13}{12}) = 12 \times 0

Calculate

2 x^{2} - 9 x + 13 = 0

Substitute a= 2,b= - 9 and c= 13 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 2 \times 13}{2 \times 2}

Simplify the expression

x = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 2 \times 13}{4}

Simplify the expression

More Steps

x = \frac{9 \pm - 23}{4}

Simplify the radical expression

More Steps

x = \frac{9 \pm 23 \times i}{4}

Separate the equation into 2 possible cases

x = \frac{9 + 23 \times i}{4} x = \frac{9 - 23 \times i}{4}

Simplify the expression

x = \frac{9}{4} + \frac{23}{4} i x = \frac{9 - 23 \times i}{4}

Simplify the expression

x = \frac{9}{4} + \frac{23}{4} i x = \frac{9}{4} - \frac{23}{4} i

Solution

x_{1} = \frac{9}{4} - \frac{23}{4} i, x_{2} = \frac{9}{4} + \frac{23}{4} i

Alternative Form

x_{1} \approx 2.25 - 1.198958 i, x_{2} \approx 2.25 + 1.198958 i

Solve the equation(The real numbers system)