Find whether the following equations have real roots. If real roots exist, find them
`5x^(2)-2x-10=0`

Explanation

Given equation is `5x^(2)-2x-10=0`
on comparing with `ax^(2)+bx+c=0` we get
`a=5,b=-2` and `c=-10`
`:.` Discriminant `D=b^(2)-4ac`
`=(-2)^(2)-4(5)(-10)`
`=4+200=204gt0`
Therefore the equation `5x^(2)-2x-10=0` has two distinct real roots.
Roots `x=(-b+-sqrt(D))/(2a)`
`=(-(-2)+-sqrt(204))/(2xx5)=(2+-2sqrt(51))/10`
`=(1+-sqrt(51))/5=(1+sqrt(51))/5,(1-sqrt(51))/5`