Multiplying LHS and RHS of the quadratic equation `5x^(2)+23x+12=0` by 5, find the roots of the equation using perfect square method.

Explanation

Given that `5x^(2)+23x+12=0`
or, `25x^(2)+115x+60=0` [Multiplying by 5]
or, `(5x)^(2)+2.5x.(23)/(2)+6=0`
or, `(5x)^(2)+2.5x.(23)/(2)+((23)/(2))^(2)=-60+((23)/(2))^(2)` [Adding `((23)/(2))^(2)` in both the sides]
or, `(5x+(23)/(2))^(2)=-60+(529)/(4)or,(5x+(23)/(2))^(2)=(-240+529)/(4)`
or, `(5x+(23)/(2))^(2)=(289)/(4)`
or, `(5x+(23)/(2))^(2)=((17)/(2))^(2)`
or, `5x+(23)/(2)=pm(17)/(2)`
or, `5x+(23)/(2)=(17)/(2)` (taking + sign) and `5x+(23)/(2)=-(17)/(2)` (taking -sign)
or, `5x=(17)/(2)-(23)/(2)" "or,5x=-(17)/(2)-(23)/(2)`
or, `5x=(17-23)/(2)" "or,5x=(-17-23)/(2)`
or, `5x=(-6)/(2)" "or,5x=(-40)/(2)`
or, `5x=-3" "or,5x=-20`
or, `x=-(3)/(5)" "or,x=-4`
Hence the roots of the quadratic equation `5x^(2)+23+12=0" are "(-(3)/(5))` and (-4).