Answer
x=$\frac{3}{2}$
Work Step by Step
Rewrite the equation in standard form.
4x$^2$=12x-9
4x$^2$-12x=-9
4x$^2$-12x+9=0
Factor the trinomial.
(2x-3)(2x-3)=0
(2x-3)$^2$=0
Set each variable factor as equal to zero and then isolate the variable to find the solutions.
2x-3=0
2x=3
x=$\frac{3}{2}$
Enter the original equation into your graphing utility to observe that the graph crosses the x-axis at $\frac{3}{2}$.