What is 2x(x-4)-3x>-2 ?

The solution to 2x(x-4)-3x>-2 is x (sqrt(105)+11)/4

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2x(x-4)-3x>-2

2 x (x - 4) - 3 x > - 2

x < \frac{- 105 + 11}{4} or x > \frac{105 + 11}{4}

Interval Notation

(- \infty, \frac{- 105 + 11}{4}) \cup (\frac{105 + 11}{4}, \infty)

Decimal Notation

x < 0.18826 \dots or x > 5.31173 \dots

Solution steps

2 x (x - 4) - 3 x > - 2

Rewrite in standard form

2 x^{2} - 11 x + 2 > 0

Complete the square

2 x^{2} - 11 x + 2 : 2 (x - \frac{11}{4})^{2} - \frac{105}{8}

2 (x - \frac{11}{4})^{2} - \frac{105}{8} > 0

Move

\frac{105}{8}

to the right side

2 (x - \frac{11}{4})^{2} > \frac{105}{8}

Divide both sides by

2

(x - \frac{11}{4})^{2} > \frac{105}{16}

For

u^{n} > a

, if

n

is even then

x - \frac{11}{4} < - \frac{105}{16} or x - \frac{11}{4} > \frac{105}{16}

x - \frac{11}{4} < - \frac{105}{16} : x < \frac{- 105 + 11}{4}

x - \frac{11}{4} > \frac{105}{16} : x > \frac{105 + 11}{4}

Combine the intervals

x < \frac{- 105 + 11}{4} or x > \frac{105 + 11}{4}

7 x^{2} - 23 x + 6

2^{x} 3^{x} \leq 7776

(\frac{5}{3})^{- 0.5}

\frac{( - 1 ) ^{4 - 1}}{5 ^{4}}

x^{3} - y^{3} - 5 x (x^{2} + x y + y^{2})

What is 2x(x-4)-3x>-2 ?
The solution to 2x(x-4)-3x>-2 is x<(-sqrt(105)+11)/4 \lor x>(sqrt(105)+11)/4