can someone help me out with these problems with explanations please

1.) if 2x^2 + p = 3x

find a value of P so that there are two rational solutions

ive already done the problem however i got anything less than 9/8 (using the discriminant and inequalities) then i checked the book for possible values and it showed up as 5/8? how does that work?

2.) The height of a firework is modelled by the equation h(t) = -at^2 + 5t where h(t) is the height of the firework and a is greater than 0

a.) factorise the function and thus determine when, in terms of a, it would land on the ground (h(t) = 0) if the firework was to follow this path completely

b.) Making the equation equal to d, solve for t in terms of a and d

3.) Can someone define the differences between an equation and an expression?

4.) A rectangle has length l and width w.

a.) write an expression for the perimeter and area in terms of l and w

b.) if the perimeter is 100m, and the area is 75m^2, change the expressions from part (a) into equations

c.) Solve the equations to find the dimensions of the rectangle correc to three decimal places

i once again attempted this and solved it wiht the values 49.24 and 0.7625 using the quadratic formula. I thought that the formula only showed the width values, how come its showing both the L and W?

Thanks guys,

Much Appreciated.