Question

Equação do 2º grau
j)$x+5=\frac{20}{x+4}$
Sendo que $(X\neq 4)$ .

Answer 1

$(x + 5) \times (x + 4) = 20 \\ {x}^{2} + 4x + 5x + 20 = 20 \\ {x}^{2} + 9x + 20 - 20 = 0 \\ {x}^{2} + 9x + 0 = 0 \\ a = 1 \\ b = 9 \\ c = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c } }{2 \times a} \\ x = \frac{ - ( + 9) + - \sqrt{ {9}^{2} - 4 \times 1 \times 0 } }{2 \times 1} \\ x = \frac{ - 9 + - \sqrt{81} }{2} \\ x = \frac{ - 9 + - 9}{2} \\ x = \frac{ - 9 + 9}{2} = \frac{0}{2} = 0 \\ x = \frac{ - 9 - 9}{2} = \frac{ - 18}{2} = - 9$