Solve y/2 y/3 = 3y/4-6

Evaluate

\frac{y}{2} \times \frac{y}{3} = (3 \times \frac{y}{4}) - 6

Multiply the terms

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\frac{y ^{2}}{6} = (3 \times \frac{y}{4}) - 6

Multiply the terms

\frac{y ^{2}}{6} = \frac{3 y}{4} - 6

Multiply both sides of the equation by LCD

\frac{y ^{2}}{6} \times 12 = (\frac{3 y}{4} - 6) \times 12

Simplify the equation

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2 y^{2} = (\frac{3 y}{4} - 6) \times 12

Simplify the equation

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2 y^{2} = 9 y - 72

Move the expression to the left side

2 y^{2} - (9 y - 72) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 y^{2} - 9 y + 72 = 0

Substitute a= 2,b= - 9 and c= 72 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 2 \times 72}{2 \times 2}

Simplify the expression

y = \frac{9 \pm ( - 9 ) ^{2} - 4 \times 2 \times 72}{4}

Simplify the expression

More Steps

y = \frac{9 \pm - 495}{4}

Solution

y \in / R

Alternative Form

No real solution

Solve the equation

Graph