Solve -5/6y^2/3=-7/9

Question

Solve the equation(The complex numbers system)

Solve using square roots

y_{1} = - \frac{70}{5} i, y_{2} = \frac{70}{5} i

Alternative Form

y_{1} \approx - 1.67332 i, y_{2} \approx 1.67332 i

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Solve using the quadratic formula

Solve using the PQ formula

y_{1} = - \frac{70}{5}, y_{2} = \frac{70}{5}

Alternative Form

y_{1} \approx - 1.67332, y_{2} \approx 1.67332

Evaluate

- \frac{5}{6} \times \frac{y ^{2}}{3} = - \frac{7}{9}

Multiply the terms

More Steps

- \frac{5 y ^{2}}{18} = - \frac{7}{9}

Rewrite the expression

- \frac{5}{18} y^{2} = - \frac{7}{9}

Move the expression to the left side

- \frac{5}{18} y^{2} + \frac{7}{9} = 0

Multiply both sides

\frac{5}{18} y^{2} - \frac{7}{9} = 0

Multiply both sides

18 (\frac{5}{18} y^{2} - \frac{7}{9}) = 18 \times 0

Calculate

5 y^{2} - 14 = 0

Substitute a= 5,b= 0 and c= - 14 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{0 \pm 0 ^{2} - 4 \times 5 ( - 14 )}{2 \times 5}

Simplify the expression

y = \frac{0 \pm 0 ^{2} - 4 \times 5 ( - 14 )}{10}

Simplify the expression

More Steps

y = \frac{0 \pm 280}{10}

Simplify the radical expression

More Steps

y = \frac{0 \pm 2 70}{10}

Separate the equation into 2 possible cases

y = \frac{0 + 2 70}{10} y = \frac{0 - 2 70}{10}

Simplify the expression

More Steps

y = \frac{70}{5} y = \frac{0 - 2 70}{10}

Simplify the expression

More Steps

y = \frac{70}{5} y = - \frac{70}{5}

Solution

y_{1} = - \frac{70}{5}, y_{2} = \frac{70}{5}

Alternative Form

y_{1} \approx - 1.67332, y_{2} \approx 1.67332

Show Solution