What is -15x^2+6x+5x-2>= 0 ?

The solution to -15x^2+6x+5x-2>= 0 is 1/3 <= x<= 2/5

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-15x^2+6x+5x-2>= 0

- 15 x^{2} + 6 x + 5 x - 2 \geq 0

\frac{1}{3} \leq x \leq \frac{2}{5}

Solution steps

- 15 x^{2} + 6 x + 5 x - 2 \geq 0

Rewrite in standard form

- 15 x^{2} + 11 x - 2 \geq 0

Factor

- 15 x^{2} + 11 x - 2 : - (3 x - 1) (5 x - 2)

- (3 x - 1) (5 x - 2) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (3 x - 1) (5 x - 2)) (- 1) \leq 0 \cdot (- 1)

Simplify

(3 x - 1) (5 x - 2) \leq 0

Identify the intervals

\frac{1}{3} \leq x \leq \frac{2}{5}

5 x^{2} + 13 x + 11 = 5

\frac{1}{\frac{3}{2}}

\frac{1}{3} x = x - 18

(\frac{2 y + 3}{4 x + 5})^{2}

- 9 + 2

What is -15x^2+6x+5x-2>= 0 ?
The solution to -15x^2+6x+5x-2>= 0 is 1/3 <= x<= 2/5