Solve 2x^2 5x -3 > 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > \frac{3 300}{10}

Alternative Form

x \in (\frac{3 300}{10}, + \infty)

Evaluate

2 x^{2} \times 5 x - 3 > 0

Multiply

More Steps

10 x^{3} - 3 > 0

Rewrite the expression

10 x^{3} - 3 = 0

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

10 x^{3} = 0 + 3

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

10 x^{3} = 3

Divide both sides

\frac{10 x ^{3}}{10} = \frac{3}{10}

Divide the numbers

x^{3} = \frac{3}{10}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{3}{10}

Calculate

x = 3 \frac{3}{10}

Simplify the root

More Steps

x = \frac{3 300}{10}

Determine the test intervals using the critical values

x < \frac{3 300}{10} x > \frac{3 300}{10}

Choose a value form each interval

x_{1} = 0 x_{2} = 2

To determine if x < \frac{3 300}{10} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{3 300}{10} is not a solution x_{2} = 2

To determine if x > \frac{3 300}{10} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{3 300}{10} is not a solution x > \frac{3 300}{10} is the solution

Solution

x > \frac{3 300}{10}

Alternative Form

x \in (\frac{3 300}{10}, + \infty)

Show Solution