Question

Encontre o valor de X

3 . (x-1) = x . (x-2)
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4 2

Answer 1

$\frac{3 \times (x - 1)}{4} = \frac{x \times (x - 2)}{2} \\ \\ \frac{3x - 3}{4} = \frac{ {x}^{2} - 2x }{2} \\ \\ 6x - 6 = 4 {x}^{2} - 8x \\ 4 {x}^{2} - 8x - 6x + 6 = 0 \\ 4 {x}^{2} - 14x + 6 = 0 \\ 2 {x}^{2} - 7x + 3 = 0 \\ x1 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x1 = \frac{7 + \sqrt{25} \:}{4} \\ \\ x1 = \frac{7 + 5}{4} = 3 \\ \\ x2 = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x2 = \frac{7 - 5}{4} = \frac{1}{2} \\ \\ solucao = 3 \: e \: \frac{1}{2}$