√x^2+7x = √7x-9
Square both sides to remove the square root on each side of the equation
(√x^2+7x)^2 = (√7x-9)^2
x^2 + 7x = 7x - 9
Now that your values aren't held by the square root you can simplify the equation
x^2 + 7x = 7x - 9
The 7x values will cancel with each other when you move either one to another side of the equation
x^2 7x - 7x = -9
x^2 = -9
now get the square root of both sides to make the x^2 value equal to x.
√x^2 = √-9
Because you're getting the square root value of a negative number your answer will be imaginary.
x = 3i