Verified answer

Resposta:

[tex]\displaystyle x=\frac{7-\sqrt{13}}{2}~~ou~~x=\frac{7+\sqrt{13}}{2}[/tex]

Explicação passo a passo:

x/(2x+6) = (x+3)/26

multiplicando cruzado

26x=(x+3)(2x+6)

aplicando a distributiva:

26x=2x²+6x+6x+18

2x²+12x-26x+18=0

2x²-14x+18=0

dividindo tudo por 2

x²-7x+9=0

[tex]\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-7x+9=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-7~e~c=9\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-7)^{2}-4(1)(9)=49-(36)=13\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-7)-\sqrt{13}}{2(1)}=\frac{7-\sqrt{13}}{2}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-7)+\sqrt{13}}{2(1)}=\frac{7+\sqrt{13}}{2}[/tex]