Solve x/12 (x-6)/6=1/2 (x-8)/8

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

Show Solution

Solve using the quadratic formula in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{21}{4} - \frac{3 15}{4} i, x_{2} = \frac{21}{4} + \frac{3 15}{4} i

Alternative Form

x_{1} \approx 5.25 - 2.904738 i, x_{2} \approx 5.25 + 2.904738 i

Evaluate

\frac{x}{12} \times \frac{x - 6}{6} = \frac{1}{2} \times \frac{x - 8}{8}

Multiply the terms

More Steps

\frac{x ( x - 6 )}{72} = \frac{1}{2} \times \frac{x - 8}{8}

Multiply the terms

More Steps

\frac{x ( x - 6 )}{72} = \frac{x - 8}{16}

Rewrite the expression

\frac{1}{72} x^{2} - \frac{1}{12} x = \frac{x - 8}{16}

Rewrite the expression

\frac{1}{72} x^{2} - \frac{1}{12} x = \frac{1}{16} x - \frac{1}{2}

Move the expression to the left side

\frac{1}{72} x^{2} - \frac{7}{48} x + \frac{1}{2} = 0

Multiply both sides

144 (\frac{1}{72} x^{2} - \frac{7}{48} x + \frac{1}{2}) = 144 \times 0

Calculate

2 x^{2} - 21 x + 72 = 0

Substitute a= 2,b= - 21 and c= 72 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{21 \pm ( - 21 ) ^{2} - 4 \times 2 \times 72}{2 \times 2}

Simplify the expression

x = \frac{21 \pm ( - 21 ) ^{2} - 4 \times 2 \times 72}{4}

Simplify the expression

More Steps

x = \frac{21 \pm - 135}{4}

Simplify the radical expression

More Steps

x = \frac{21 \pm 3 15 \times i}{4}

Separate the equation into 2 possible cases

x = \frac{21 + 3 15 \times i}{4} x = \frac{21 - 3 15 \times i}{4}

Simplify the expression

x = \frac{21}{4} + \frac{3 15}{4} i x = \frac{21 - 3 15 \times i}{4}

Simplify the expression

x = \frac{21}{4} + \frac{3 15}{4} i x = \frac{21}{4} - \frac{3 15}{4} i

Solution

x_{1} = \frac{21}{4} - \frac{3 15}{4} i, x_{2} = \frac{21}{4} + \frac{3 15}{4} i

Alternative Form

x_{1} \approx 5.25 - 2.904738 i, x_{2} \approx 5.25 + 2.904738 i

Show Solution