Question

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

Answer 1

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

Explanation:

`((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`

quadratic formula

`:.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`