X= square root of 10x-24

√10x-24 = x

Step by step solution :

STEP
1
:
Isolate the square root on the left hand side

Radical already isolated
√10x-24 = x

STEP
2
:
Eliminate the radical on the left hand side

Raise both sides to the second power
(√10x-24)2 = (x)2

After squaring
10x-24 = x2

STEP
3
:
Solve the quadratic equation

Rearranged equation
x2 - 10x + 24 = 0

This equation has two rational roots:
{x1, x2}={6, 4}

STEP
4
:
Check that the first solution is correct

Original equation
√10x-24 = x

Plug in 6 for x
√10•(6)-24 = (6)

Simplify
√36 = 6
Solution checks !!
Solution is:
x = 6

STEP
5
:
Check that the second solution is correct

Original equation
√10x-24 = x

Plug in 4 for x
√10•(4)-24 = (4)

Simplify
√16 = 4
Solution checks !!
Solution is:
x = 4