calculus 2 pls help

Question

Find consumer's surplus at the market equilibrium point given that the demand function is

 and the supply function is . p= sqrt(676-80x) and the supply function is p=x+8

Answer 1

Find equlibrium:√ (676 -80x) = x + 8; 676 - 80x = x² + 16x + 64; x² + 96x - 612 = 0; (x +102)(x - 6) = 0;

x = 6 or x = -102. So equlibrium demand x = 6 and price p = 6 + 8 = 14.

Consumer surplus CS = ∫₀⁶[√(676 - 80x) - 14]dx = [- 1/80·2/3·(676 - 80x)^3/2 - 14x]₀⁶ = - 1/120(2744 - 17576) - 84 = 39.6