Thank you for the opportunity to help you with your question!

f(x) = 5 − 3x + 4x2

f(a) = 5 − 3a + 4a^2

f(a+h) = 5 − 3(a+h) + 4(a+h)^2 = 5 − 3a-3h + 4a^2+4h^2+ 8ah

[f(a+h) - f(a)]/h =  (5 − 3a-3h + 4a^2+4h^2+ 8ah - 5+ 3a-4a^2 ) /h

                        = (-3h + 4h^2 +8ah)/h = 4h+8a-3

please let me know if you have any problem in understanding the solution or need more clarification and details . i will be more happy to help you
please best me in review 
best of luck :)