Question 604301
First Part	84	miles												
Second Part	22	miles												
														
First Part	x			mph										
Second Part	x		-5	mph										
Total time		2	hours											
First Part	time 	84	/	x										
Second Part	time 	22	/	(	x	-5	)							
														
Time first part + time second part =			2	hours										
														
84/x+22	/(x-5)	=2		
LCD =	(x)*(x-5)						
multiply the equation by the LCD														
we get														
84*(x	-5)+22	x=	2		
84x-420	+22x=2X^2-10
116	x+	-420	=	2	X^2									
2	X^2	-116	x+	420			=	0						
2	X^2+	-116	x+	420	=		=	0						
/	2													
2	X^2	-116	x+	420	=	0								
														
Find the roots of the equation by quadratic formula														
														
a=	2	b=	-116	c=	420									
														
b^2-4ac=	13456	-	3360											
b^2-4ac=	10096		
{{{sqrt(	10096	)}}}=	100.48							
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}														
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}														
x1=(	116	+	100.48	)/	4									
x1=	54.12													
x2=(	116	-100.48	) /	4										
x2=	3.88													
x2 is not possible

so speed = 54.12 mph I part
49.12 mph II part