How do you solve #\frac { 4} { x - 3} = \frac { x + 5} { 5} ]#?

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Answer 1 · 2018-01-11T17:57:57

#x_1=5# and #x_2=-7#

#4/(x-3)=(x+5)/5#

Perform this
#4/(x-3) #χ# (x+5)/5#

#<=># #4*5=(x-3)(x+5)# #<=>#

#20=x^2+5x-3x-15 <=>#

#x^2+2x-35=0#

Discriminant will be #Δ=b^2-4ac=4-4*1*(-35)=140+4=144#

#x_(1,2)=(-b+-sqrt(Δ))/(2α)# so

#x_1=(-2+12)/2=5#

#x_2=(-2-12)/2=-14/2=-7#

As a result the roots are #x_1=5# and #x_2=-7#