Solve 2/(3t^2 2) = 1/5

Question

Solve the equation

t_{1} = - \frac{15}{3}, t_{2} = \frac{15}{3}

Alternative Form

t_{1} \approx - 1.290994, t_{2} \approx 1.290994

Evaluate

\frac{2}{3 t ^{2} \times 2} = \frac{1}{5}

Find the domain

More Steps

Evaluate

3 t^{2} \times 2 \neq = 0

Multiply the terms

6 t^{2} \neq = 0

Rewrite the expression

t^{2} \neq = 0

The only way a power can not be 0 is when the base not equals 0

t \neq = 0

\frac{2}{3 t ^{2} \times 2} = \frac{1}{5}, t \neq = 0

Reduce the fraction

More Steps

Evaluate

\frac{2}{3 t ^{2} \times 2}

Multiply the terms

\frac{2}{6 t ^{2}}

Reduce the fraction

\frac{1}{3 t ^{2}}

\frac{1}{3 t ^{2}} = \frac{1}{5}

Rewrite the expression

3 t^{2} = 5

Divide both sides

\frac{3 t ^{2}}{3} = \frac{5}{3}

Divide the numbers

t^{2} = \frac{5}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

t = \pm \frac{5}{3}

Simplify the expression

More Steps

Evaluate

\frac{5}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5}{3}

Multiply by the Conjugate

\frac{5 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

5 \times 3

The product of roots with the same index is equal to the root of the product

5 \times 3

Calculate the product

15

\frac{15}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{15}{3}

t = \pm \frac{15}{3}

Separate the equation into 2 possible cases

t = \frac{15}{3} t = - \frac{15}{3}

Check if the solution is in the defined range

t = \frac{15}{3} t = - \frac{15}{3}, t \neq = 0

Find the intersection of the solution and the defined range

t = \frac{15}{3} t = - \frac{15}{3}

Solution

t_{1} = - \frac{15}{3}, t_{2} = \frac{15}{3}

Alternative Form

t_{1} \approx - 1.290994, t_{2} \approx 1.290994

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