Solve 5t^2/2t=4/5

$$\frac { 5 t ^ { 2 } } { 2 t } = \frac { 4 } { 5 }$$

Solve for t

$$t=\frac{8}{25}=0.32$$

Steps Using Factoring

Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10t, the least common multiple of 2t,5.

$$5\times 5t^{2}=8t$$

Multiply 5 and 5 to get 25.

$$25t^{2}=8t$$

Subtract 8t from both sides.

$$25t^{2}-8t=0$$

Factor out t.

$$t\left(25t-8\right)=0$$

To find equation solutions, solve t=0 and 25t-8=0.

$$t=0 t=\frac{8}{25}$$

Variable t cannot be equal to 0.

$$t=\frac{8}{25}$$

Steps Using the Quadratic Formula

Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10t, the least common multiple of 2t,5.

$$5\times 5t^{2}=8t$$

Multiply 5 and 5 to get 25.

$$25t^{2}=8t$$

Subtract 8t from both sides.

$$25t^{2}-8t=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, -8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 25}$$

Take the square root of \left(-8\right)^{2}.

$$t=\frac{-\left(-8\right)±8}{2\times 25}$$

The opposite of -8 is 8.

$$t=\frac{8±8}{2\times 25}$$

Multiply 2 times 25.

$$t=\frac{8±8}{50}$$

Now solve the equation t=\frac{8±8}{50} when ± is plus. Add 8 to 8.

$$t=\frac{16}{50}$$

Reduce the fraction \frac{16}{50} to lowest terms by extracting and canceling out 2.

$$t=\frac{8}{25}$$

Now solve the equation t=\frac{8±8}{50} when ± is minus. Subtract 8 from 8.

$$t=\frac{0}{50}$$

Divide 0 by 50.

$$t=0$$

The equation is now solved.

$$t=\frac{8}{25} t=0$$

Variable t cannot be equal to 0.

$$t=\frac{8}{25}$$

Steps for Completing the Square

Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10t, the least common multiple of 2t,5.

$$5\times 5t^{2}=8t$$

Multiply 5 and 5 to get 25.

$$25t^{2}=8t$$

Subtract 8t from both sides.

$$25t^{2}-8t=0$$

Divide both sides by 25.

$$\frac{25t^{2}-8t}{25}=\frac{0}{25}$$

Dividing by 25 undoes the multiplication by 25.

$$t^{2}-\frac{8}{25}t=\frac{0}{25}$$

Divide 0 by 25.

$$t^{2}-\frac{8}{25}t=0$$

Divide -\frac{8}{25}, the coefficient of the x term, by 2 to get -\frac{4}{25}. Then add the square of -\frac{4}{25} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$t^{2}-\frac{8}{25}t+\left(-\frac{4}{25}\right)^{2}=\left(-\frac{4}{25}\right)^{2}$$

Square -\frac{4}{25} by squaring both the numerator and the denominator of the fraction.

$$t^{2}-\frac{8}{25}t+\frac{16}{625}=\frac{16}{625}$$

Factor t^{2}-\frac{8}{25}t+\frac{16}{625}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-\frac{4}{25}\right)^{2}=\frac{16}{625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(t-\frac{4}{25}\right)^{2}}=\sqrt{\frac{16}{625}}$$

Simplify.

$$t-\frac{4}{25}=\frac{4}{25} t-\frac{4}{25}=-\frac{4}{25}$$

Add \frac{4}{25} to both sides of the equation.

$$t=\frac{8}{25} t=0$$

Variable t cannot be equal to 0.

$$t=\frac{8}{25}$$