Solve 3y^2-5y-10+15y-6y^2

Question

Simplify the expression

- 3 y^{2} + 10 y - 10

Show Solution

y_{1} = \frac{5}{3} - \frac{5}{3} i, y_{2} = \frac{5}{3} + \frac{5}{3} i

Alternative Form

y_{1} \approx 1. \dot{6} - 0.745356 i, y_{2} \approx 1. \dot{6} + 0.745356 i

Evaluate

3 y^{2} - 5 y - 10 + 15 y - 6 y^{2}

To find the roots of the expression,set the expression equal to 0

3 y^{2} - 5 y - 10 + 15 y - 6 y^{2} = 0

Add the terms

More Steps

3 y^{2} + 10 y - 10 - 6 y^{2} = 0

Subtract the terms

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- 3 y^{2} + 10 y - 10 = 0

Multiply both sides

3 y^{2} - 10 y + 10 = 0

Substitute a= 3,b= - 10 and c= 10 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 3 \times 10}{2 \times 3}

Simplify the expression

y = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 3 \times 10}{6}

Simplify the expression

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y = \frac{10 \pm - 20}{6}

Simplify the radical expression

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y = \frac{10 \pm 2 5 \times i}{6}

Separate the equation into 2 possible cases

y = \frac{10 + 2 5 \times i}{6} y = \frac{10 - 2 5 \times i}{6}

Simplify the expression

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y = \frac{5}{3} + \frac{5}{3} i y = \frac{10 - 2 5 \times i}{6}

Simplify the expression

More Steps

y = \frac{5}{3} + \frac{5}{3} i y = \frac{5}{3} - \frac{5}{3} i

Solution

y_{1} = \frac{5}{3} - \frac{5}{3} i, y_{2} = \frac{5}{3} + \frac{5}{3} i

Alternative Form

y_{1} \approx 1. \dot{6} - 0.745356 i, y_{2} \approx 1. \dot{6} + 0.745356 i

Show Solution