Solve 3t^2=19200-640t

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

t_{1} = - 240, t_{2} = \frac{80}{3}

Alternative Form

t_{1} = - 240, t_{2} = 26. \dot{6}

Evaluate

3 t^{2} = 19200 - 640 t

Move the expression to the left side

3 t^{2} - 19200 + 640 t = 0

Factor the expression

More Steps

Evaluate

3 t^{2} - 19200 + 640 t

Reorder the terms

3 t^{2} + 640 t - 19200

Rewrite the expression

3 t^{2} + (- 80 + 720) t - 19200

Calculate

3 t^{2} - 80 t + 720 t - 19200

Rewrite the expression

t \times 3 t - t \times 80 + 240 \times 3 t - 240 \times 80

Factor out t from the expression

t (3 t - 80) + 240 \times 3 t - 240 \times 80

Factor out 240 from the expression

t (3 t - 80) + 240 (3 t - 80)

Factor out 3 t - 80 from the expression

(t + 240) (3 t - 80)

(t + 240) (3 t - 80) = 0

When the product of factors equals 0,at least one factor is 0

3 t - 80 = 0 t + 240 = 0

Solve the equation for t

More Steps

Evaluate

3 t - 80 = 0

Move the constant to the right-hand side and change its sign

3 t = 0 + 80

Removing 0 doesn't change the value,so remove it from the expression

3 t = 80

Divide both sides

\frac{3 t}{3} = \frac{80}{3}

Divide the numbers

t = \frac{80}{3}

t = \frac{80}{3} t + 240 = 0

Solve the equation for t

More Steps

Evaluate

t + 240 = 0

Move the constant to the right-hand side and change its sign

t = 0 - 240

Removing 0 doesn't change the value,so remove it from the expression

t = - 240

t = \frac{80}{3} t = - 240

Solution

t_{1} = - 240, t_{2} = \frac{80}{3}

Alternative Form

t_{1} = - 240, t_{2} = 26. \dot{6}

Show Solution