From the text of the task we can write the equation:
3 x 2 = 2 ( x + 4 ) 3 x 2 = 2 x + 8 3 x 2 − 2 x − 8 = 0 Δ = ( − 2 ) 2 − 4.3. ( − 8 ) = 4 + 96 = 100 x = 2.3 2 ± 100 = 6 2 ± 10 x 1 = 6 2 − 10 = − 6 8 = − 3 4 x 2 = 2.3 2 + 10 = 6 12 = 2
3 x 2 = 2 ( x + 4 ) 3 x 2 = 2 x + 8 3 x 2 − 2 x − 8 = 0 3 x 2 − 6 x + 4 x − 8 = 0 3 x ( x − 2 ) + 4 ( x − 2 ) = 0 ( 3 x + 4 ) ( x − 2 ) = 0 x = − 3 4 ∨ x = 2
The equation representing the statement is 3 x 2 = 2 ( x + 4 ) . After rearranging, we get 3 x 2 − 2 x − 8 = 0 which can be solved using the quadratic formula. The positive solution for x is 2.
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