x + 4/x - 1 = 4/3
x^2 + 4 - x = 4x/3
x^2 + 4 -x -4x/3 = 0
x^2 + 4 - (3x + 4x)/3 = 0
x^2 + 4 - 7x/3 = 0
now use the quadratic equation where a = 1, b = -7/3, and c = 4
you may want to multiply through by 3 first to get rid of the fractions. it will be easier.
3x^2 - 7x + 12 = 0
now a = 3, b = -7 and c = 12
quadratic solution is
x = [-b +/- sqrt ( b^2 - 4*a*c)]/2*a