Solve 5(w-2)=-3(w^2)

Evaluate

5 (w - 2) = - 3 w^{2}

Swap the sides

- 3 w^{2} = 5 (w - 2)

Expand the expression

More Steps

- 3 w^{2} = 5 w - 10

Move the expression to the left side

- 3 w^{2} - 5 w + 10 = 0

Multiply both sides

3 w^{2} + 5 w - 10 = 0

Substitute a= 3,b= 5 and c= - 10 into the quadratic formula w = \frac{- b \pm b ^{2} - 4 a c}{2 a}

w = \frac{- 5 \pm 5 ^{2} - 4 \times 3 ( - 10 )}{2 \times 3}

Simplify the expression

w = \frac{- 5 \pm 5 ^{2} - 4 \times 3 ( - 10 )}{6}

Simplify the expression

More Steps

w = \frac{- 5 \pm 145}{6}

Separate the equation into 2 possible cases

w = \frac{- 5 + 145}{6} w = \frac{- 5 - 145}{6}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

w = \frac{- 5 + 145}{6} w = - \frac{5 + 145}{6}

Solution

w_{1} = - \frac{5 + 145}{6}, w_{2} = \frac{- 5 + 145}{6}

Alternative Form

w_{1} \approx - 2.840266, w_{2} \approx 1.173599

Solve the quadratic equation