Given 4x square+3x+5=0
x square +3/4x +5/4=0
x square +3/4x= -5/4
x square+3/4x+(3/8)square = -5/4 + (3/8)square
(x+3/8)square = -5/4 + +9/64
( x + 3/8 ) square = -71/64 < 0
but (x + 3/8 )square cannot be negative for any real value of x. so, there is no real value of x satisfying the given equation.
therefore, the given equation has no real roots....
hope it help u................