Find x for the triangle when it's a right triangle

Just use the Pythagorean theorem.

a^2 + b^2 = c^2
4^2 + x^2 = (2x-1)^2
16+x^2=(2x-1)(2x-1)
16+x^2=4x^2-4x+1
0=3x^2-4x-15
0=(3x+5)(x-3)
3x+5=0    x-3=0
3x= -5       x=3
x= -5/3      x=3

Since x can't be a negative number when it comes to distance or the length of a triangle, the answer must be x=3.