Solve \dfrac{d-5}{d-3} \dfrac{5d-2}{4d-12} = \dfrac{3 - ScanMath

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Type your math problem... \dfrac{d-5}{d-3} \dfrac{5d-2}{4d-12} = \dfrac{3}{2}

Question

Solve the equation

d \in / R

Alternative Form

No real solution

Evaluate

\frac{d - 5}{d - 3} \times \frac{5 d - 2}{4 d - 12} = \frac{3}{2}

Multiply the terms

\frac{( d - 5 ) ( 5 d - 2 )}{( d - 3 ) ( 4 d - 12 )} = \frac{3}{2}

Cross multiply

(d - 5) (5 d - 2) \times 2 = (d - 3) (4 d - 12) \times 3

Simplify the equation

2 (d - 5) (5 d - 2) = (d - 3) (4 d - 12) \times 3

Simplify the equation

2 (d - 5) (5 d - 2) = 3 (d - 3) (4 d - 12)

Rewrite the expression

2 (d - 5) (5 d - 2) = 2 \times 3 (d - 3) (2 d - 6)

Evaluate

(d - 5) (5 d - 2) = 3 (d - 3) (2 d - 6)

Calculate

More Steps

5 d^{2} - 27 d + 10 = 3 (d - 3) (2 d - 6)

Calculate

More Steps

5 d^{2} - 27 d + 10 = 6 d^{2} - 36 d + 54

Move the expression to the left side

5 d^{2} - 27 d + 10 - (6 d^{2} - 36 d + 54) = 0

Calculate the sum or difference

More Steps

- d^{2} + 9 d - 44 = 0

Multiply both sides

d^{2} - 9 d + 44 = 0

Substitute a= 1,b= - 9 and c= 44 into the quadratic formula d = \frac{- b \pm b ^{2} - 4 a c}{2 a}

d = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 44}{2}

Simplify the expression

More Steps

d = \frac{9 \pm - 95}{2}

Solution

d \in / R

Alternative Form

No real solution

Show Solution

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