+128473 Let sqrt ( 4x - 3) = a
So we have
a + 10 / a = 7 multiply through by a
a^2 + 10 = 7a rearrange as
a^2 - 7a + 10 = 0 factor as
(a - 5) ( a - 2) = 0 set each factor to 0 and solve for a
a - 5 = 0 a - 2 = 0
a = 5 a = 2
So
sqrt ( 4x - 3) = 5 or sqrt (4x - 3) = 2
square both sides
4x - 3 = 25 4x - 3 = 4
4x = 28 4x = 7
x = 7 x = 7/4 are the two solutions
