Answer:
A = [- 2Bl + U^2 +/- √((2BL - U^2)^2 - 4B^2L^2) ] / 2L
Step-by-step explanation:
L = U^2A / (A + B)^2
U^2 A = L(A^2 + 2AB + B^2)
U^2 A = LA^2 + 2ABL + B^2L
LA^2 + 2ABL - U^2A + B^2 L = 0
LA^2 + (2BL - U^2)A + B^2L = 0
Using the quadratic formula
A = [- (2BL - U^2) +/- √[(2BL - U^2)^2 - 4*L*B^2L] / 2L
A = [- 2BL + U^2 +/- √[(2BL - U^2)^2 - 4B^2L^2) ] / 2L
