If two times the square of a positive number is $9$ more than three times of the number. Find the number.

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Solution

Let $x$ be the number then $x > 0$ .
Given, two times the square of a positive number is $9$ more than three times of the number.
Then $2 x^{2} = 3 x + 9$
or, $2 x^{2} - 3 x - 9 = 0$
or, $2 x^{2} - 6 x + 3 x - 9 = 0$
or, $2 x (x - 3) + 3 (x - 3) = 0$
or, $(2 x + 3) (x - 3) = 0$
or, $x = 3$ [ Since $x > 0$ ]
So the number is $3$ .

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If two times the square of a positive number is 9 more than three times of the number. Find the number.

Let x be the number then x>0.Given, two times the square of a positive number is 9 more than three times of the number.Then 2x2=3x+9or, 2x2−3x−9=0or, 2x2−6x+3x−9=0or, 2x(x−3)+3(x−3)=0or, (2x+3)(x−3)=0or, x=3 [ Since x>0]So the number is 3.

If two times the square of a positive number is $9$ more than three times of the number. Find the number.