Solve each radical equation. square root 5x^2-3x=2x

Answer 1

sqrt(5x^2 - 3x) = 2x
First thing to do is to square both sides of the equation, then solve for x:
[sqrt(5x^2 - 3x)]^2 = (2x)^2
5x^2 - 3x = 4x^2
x^2 - 3x = 0
x(x - 3) = 0
x = 0
x = 3
Then to check if it really satisfies the original equation, substitute the x values back to the original:
x = 0:
sqrt(5(0)^2 - 3(0)) = 2(0)
sqrt(0 - 0) = 0
0 = 0
Thus x is indeed equal to 0.

x = 3:
sqrt(5(3)^2 - 3(3)) = 2(3)
sqrt(45 - 9) = 6
sqrt(36) = 6
6 = 6
Thus x is indeed equal to 3.

Hope this helps~ :3