+128474 √[ 4x - 3 ] + 10 / √[ 4x - 3] = 7
Let √ [ 4x - 3] = a
So we have
a + 10/a = 7 multiply through by a
a^2 + 10 = 7a subtract 7a from both sides
a^2 - 7a + 10 = 0 factor
( a - 5) (a - 2) = 0
Setting each factor to 0 and solving produces a = 5 or a = 2
So.....
√ [ 4x - 3] = 5 square both sides
4x - 3 = 25 add 3 to both sides
4x = 28 divide both sides by 2
x = 7
or
√ [ 4x - 3] = 2 square bot sides
4x - 3 = 4 add 3 to both sides
4x = 7 divide both sides by 4
x = 7/4
