Solve the following quatratic equations by completing square method :
`5x^(2)=4x+7`

Answer

`2-(sqrt39)/(5),2+(sqrt30)/(5)` are the roots of the given quadratic equation.

Explanation

`5x^(2)=4x+7`
`:.5x^(2)-4x-7=0`
`:.x^(2)-(4x)/(5)-(7)/(5)=0" "......` (Dividing by 5)
Comparing `x^(2)-(4x)/(5)" with "x^(2)-2xy`
`:.y=(2)/(5):.y^(2)=(4)/(25)`
`:.x^(2)-(4x)/(5)+(4)/(25)` is a perfect square trinomial.
`x^(2)-(4x)/(5)+(7)/(5)=0`
`:.x^(2)-(4x)/(5)+(4)/(25)-(4)/(25)-(7)/(5)=0`
`:.(x-(2)/(5))^(2)-((4)/(25)+(7)/(5))=0`
`:.(x-(2)/(5))^(2)-((4+35)/(25))=0`
`:.(x-(2)/(5))^(2)-((39)/(25))=0`
`:.(x-(2)/(5))^(2)-((sqrt39)/(5))^(2)=0`
`:.(x-(2)/(5)+(sqrt39)/(5))(x-(2)/(5)-(sqrt39)/(5))=0`
`:.x-(2)/(5)+(sqrt39)/(5)=0orx-(2)/(5)-(sqrt39)/(5)=0`
`:.x-(2)/(5)-(sqrt39)/(5)orx=(2)/(5)+(sqrt39)/(5)`
`:.x=(2-sqrt39)/(5)orx=(2+sqrt39)/(5)`