Hey Friends!! solve this quest!_______________________________________

1.	Hey Friends!! solve this quest!______________________________________________Q) If f:R->R and g:R->R are defined by f(x)=2x+3 and g(x)=x²+7, then the values of x such that g(f(x))=8 are:Options are:i) 1,2ii) -1,2iii) -1,-2iv) 1,-2___________________________________________Please answer it accurately and BEWARE OF SPAMMING!!
Answer» $\red{\bold{ANSWER}}$ $\rm{-1\:\:,-2}$ $\mathbb{EXPLANATION}$ $\rm{F:R\rightarrow\:R}$ $\rm{F\left(x\right)=2x+3}$ $\boxed{\mathbb{AND}}$ $\rm{G:R\rightarrow\:R}$ $\rm{G\left(x\right)=x^2+7}$ $\underline{\mathbb{GIVEN}}$ $\rm{G\left(F\left(x\right)\right)=8}$ $\rm{G\left(2x+3\right)=8}$ $\rm{\left(\left(2x+3\right)^2+7\right)=8}$ $\rm{4x^2+9+12x+7-8=0}$ $\rm{4x^2+12x+8=0}$ $\rm{x^2+3x+2=0}$ $\rm{x^2+2x+x+2=0}$ $\rm{x\left(x+2\right)+1\left(x+2\right)=0}$ $\rm{\left(x+2\right)\times\left(x+1\right)=0}$ $\rm{x=-2\:\:OR\:\:x=-1}$ $\therefore$ $\rm{x=-2,-1}$ $\boxed{\rm{\mathbb{HENCE,\:OPTION\:THIRD\:IS\:CORRECT}}}$