Solve 06t-160/3*5*10^-4/4*10^-3t^2=-204

$$06 t - \frac { \frac { 160 } { 3 } \times 5 \times 10 ^ { - 4 } } { 4 \times 10 ^ { - 3 } } t ^ { 2 } = - 204$$

Solve for t

$$t = \frac{3 \sqrt{85}}{5} \approx 5.531726674$$

$$t = -\frac{3 \sqrt{85}}{5} \approx -5.531726674$$

Steps by Finding Square Root

Multiply 0 and 6 to get 0.

$$0t-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

Anything times zero gives zero.

$$0-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$0-\frac{5\times \frac{160}{3}}{4\times 10^{1}}t^{2}=-204$$

Multiply 5 and \frac{160}{3} to get \frac{800}{3}.

$$0-\frac{\frac{800}{3}}{4\times 10^{1}}t^{2}=-204$$

Calculate 10 to the power of 1 and get 10.

$$0-\frac{\frac{800}{3}}{4\times 10}t^{2}=-204$$

Multiply 4 and 10 to get 40.

$$0-\frac{\frac{800}{3}}{40}t^{2}=-204$$

Express \frac{\frac{800}{3}}{40} as a single fraction.

$$0-\frac{800}{3\times 40}t^{2}=-204$$

Multiply 3 and 40 to get 120.

$$0-\frac{800}{120}t^{2}=-204$$

Reduce the fraction \frac{800}{120} to lowest terms by extracting and canceling out 40.

$$0-\frac{20}{3}t^{2}=-204$$

Anything plus zero gives itself.

$$-\frac{20}{3}t^{2}=-204$$

Multiply both sides by -\frac{3}{20}, the reciprocal of -\frac{20}{3}.

$$t^{2}=-204\left(-\frac{3}{20}\right)$$

Multiply -204 and -\frac{3}{20} to get \frac{153}{5}.

$$t^{2}=\frac{153}{5}$$

Take the square root of both sides of the equation.

$$t=\frac{3\sqrt{85}}{5} t=-\frac{3\sqrt{85}}{5}$$

Steps Using the Quadratic Formula

Multiply 0 and 6 to get 0.

$$0t-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

Anything times zero gives zero.

$$0-\frac{\frac{160}{3}\times 5\times 10^{-4}}{4\times 10^{-3}}t^{2}=-204$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$0-\frac{5\times \frac{160}{3}}{4\times 10^{1}}t^{2}=-204$$

Multiply 5 and \frac{160}{3} to get \frac{800}{3}.

$$0-\frac{\frac{800}{3}}{4\times 10^{1}}t^{2}=-204$$

Calculate 10 to the power of 1 and get 10.

$$0-\frac{\frac{800}{3}}{4\times 10}t^{2}=-204$$

Multiply 4 and 10 to get 40.

$$0-\frac{\frac{800}{3}}{40}t^{2}=-204$$

Express \frac{\frac{800}{3}}{40} as a single fraction.

$$0-\frac{800}{3\times 40}t^{2}=-204$$

Multiply 3 and 40 to get 120.

$$0-\frac{800}{120}t^{2}=-204$$

Reduce the fraction \frac{800}{120} to lowest terms by extracting and canceling out 40.

$$0-\frac{20}{3}t^{2}=-204$$

Anything plus zero gives itself.

$$-\frac{20}{3}t^{2}=-204$$

Add 204 to both sides.

$$-\frac{20}{3}t^{2}+204=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{20}{3} for a, 0 for b, and 204 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{20}{3}\right)\times 204}}{2\left(-\frac{20}{3}\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{20}{3}\right)\times 204}}{2\left(-\frac{20}{3}\right)}$$

Multiply -4 times -\frac{20}{3}.

$$t=\frac{0±\sqrt{\frac{80}{3}\times 204}}{2\left(-\frac{20}{3}\right)}$$

Multiply \frac{80}{3} times 204.

$$t=\frac{0±\sqrt{5440}}{2\left(-\frac{20}{3}\right)}$$

Take the square root of 5440.

$$t=\frac{0±8\sqrt{85}}{2\left(-\frac{20}{3}\right)}$$

Multiply 2 times -\frac{20}{3}.

$$t=\frac{0±8\sqrt{85}}{-\frac{40}{3}}$$

Now solve the equation t=\frac{0±8\sqrt{85}}{-\frac{40}{3}} when ± is plus.

$$t=-\frac{3\sqrt{85}}{5}$$

Now solve the equation t=\frac{0±8\sqrt{85}}{-\frac{40}{3}} when ± is minus.

$$t=\frac{3\sqrt{85}}{5}$$

The equation is now solved.

$$t=-\frac{3\sqrt{85}}{5} t=\frac{3\sqrt{85}}{5}$$