How do you solve #\frac { ( x - 3) ( x + 4) } { 5} - \frac { 14x + 35} { 6} = \frac { ( 52x + 5) } { 10}#?

Question

960 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-28T17:26:30

#color(magenta)(x=(55+-4sqrt3418)/3#

#((x-3)(x+4))/5-(14x+35)/6=((52x+5))/10#

#:.(6(x^2+x-12)-5(14x+35)=3(52x+5))/30#

multiply both sides by #30#

#6x^2+6x-72-70x-175=156x+15#

#:.6x^2+6x-72-70x-175-156x-15=0#

#:.6x^2-220x-262=0#

#:.x=(-b+-sqrt(b^2-4ac))/(2a)#

#:.x=(-(-220)+-sqrt((-220)^2-4(6)(-262)))/(2(6)#

#:.x=(cancel220^color(magenta)55+-sqrt54688)/cancel12^(color(magenta)3)#

#:.x=(55+-sqrt(1709*2*2*2*2*2))/3#

#:.x=(55+-4sqrt(1709*2))/3#

#:.color(magenta)(x=(55+-4sqrt3418)/3#