What is 2x^2-6x+3<0 ?

The solution to 2x^2-6x+3<0 is (-sqrt(3)+3)/2 <x<(sqrt(3)+3)/2

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2x^2-6x+3<0

2 x^{2} - 6 x + 3 < 0

\frac{- 3 + 3}{2} < x < \frac{3 + 3}{2}

Interval Notation

(\frac{- 3 + 3}{2}, \frac{3 + 3}{2})

Decimal Notation

0.63397 \dots < x < 2.36602 \dots

Solution steps

2 x^{2} - 6 x + 3 < 0

Complete the square

2 x^{2} - 6 x + 3 : 2 (x - \frac{3}{2})^{2} - \frac{3}{2}

2 (x - \frac{3}{2})^{2} - \frac{3}{2} < 0

Move

\frac{3}{2}

to the right side

2 (x - \frac{3}{2})^{2} < \frac{3}{2}

Divide both sides by

2

(x - \frac{3}{2})^{2} < \frac{3}{4}

For

u^{n} < a

, if

n

is even then

- \frac{3}{4} < x - \frac{3}{2} < \frac{3}{4}

a < u < b

then

a < u and u < b

- \frac{3}{4} < x - \frac{3}{2} and x - \frac{3}{2} < \frac{3}{4}

- \frac{3}{4} < x - \frac{3}{2} : x > \frac{- 3 + 3}{2}

x - \frac{3}{2} < \frac{3}{4} : x < \frac{3 + 3}{2}

Combine the intervals

x > \frac{- 3 + 3}{2} and x < \frac{3 + 3}{2}

Merge Overlapping Intervals

\frac{- 3 + 3}{2} < x < \frac{3 + 3}{2}

3 y^{2} = 48

8 z - 1 = 11

\frac{x}{12} + 6 = 8

3 y^{3} + 5 y^{2} + 3 y + 5

24 x y^{2} + 40 y

What is 2x^2-6x+3<0 ?
The solution to 2x^2-6x+3<0 is (-sqrt(3)+3)/2 <x<(sqrt(3)+3)/2