Find whether the following equations have real roots. If real roots exist, find them
`-2x^(2)+3x+2=0`

Explanation

Given equation is `-2x^(2)+3x+2=0`
on comparing with `ax^(2)+bx+c=0` we get
`a=-2,b=3` and `c=2`.
`:.` Discriminant `D=b^(2)-4ac`
`=(3)^(2)-4(-2)(2)`
`=9+16=25gt0`
Therefore, the equation `-2x^(2)+3x+2=0` has two distinct real roots because we know that if the equation `ax^(2)+bx+c=0` has its discriminant greater than zero, then it has two distinct real roots.
Roots `x=(-b+-sqrt(D))/(2a)=(-3+-sqrt(25))/(2(-2))`
`=(-3+-5)/(-4)=(-3+5)/(-4),(-3-5)/(-4)`
`=2/(-4),(-8)/(-4)=-1/2,2`