To solve the radical equation √4z²-13z+9+3=3z, we need to get rid of the radical sign in order to isolate the variable.
First, we can add 9 to both sides to get:
√4z²-13z+12=3z+9
Then we can square both sides of the equation:
4z²-13z+12 = 9z²+27z+81
Now, we can rearrange the equation to get:
9z²-40z+69 = 0
Now we can use the quadratic formula to find the solutions for z:
z = (40 ± √(40²-4969)) / 2*9
z = (40 ± √(1600-2772)) / 18
z = (40 ± √(-1172)) / 18
Since the square root of a negative number is an imaginary number, this equation has no real solutions, which means that there are no values of z that will make the equation true.
So the radical equation √4z²-13z+9+3=3z doesn't have any solution.