(4a-3)=a+33/a+1

Solution for (4a-3)=a+33/a+1 equation:

D( a )

a = 0

a = 0

a = 0

a in (-oo:0) U (0:+oo)

4*a-3 = a+33/a+1 // - a+33/a+1

4*a-a-(33/a)-3-1 = 0

4*a-a-33*a^-1-3-1 = 0

3*a^1-33*a^-1-4*a^0 = 0

(3*a^2-4*a^1-33*a^0)/(a^1) = 0 // * a^2

a^1*(3*a^2-4*a^1-33*a^0) = 0

a^1

3*a^2-4*a-33 = 0

3*a^2-4*a-33 = 0

DELTA = (-4)^2-(-33*3*4)

DELTA = 412

DELTA > 0

a = (412^(1/2)+4)/(2*3) or a = (4-412^(1/2))/(2*3)

a = (2*103^(1/2)+4)/6 or a = (4-2*103^(1/2))/6

a in { (4-2*103^(1/2))/6, (2*103^(1/2)+4)/6} 

a in { (4-2*103^(1/2))/6, (2*103^(1/2)+4)/6 }