Finding value of x with polynomials in a triangle

Question

I need help with a question which includes finding the value of x with polynomials in a right triangle. The hypotenuse of the triangle is (5x-6) and the two other sides are (4x-7) and (3x-1)

Answer 1

$$ (5x-6)^2=(4x-7)^2 + (3x-1)^2\\ 25x^2 + 36 - 60x = 16x^2 + 49 - 56x + 9x^2 + 1 - 6x\\ 25x^2 + 36 - 60x = 25x^2 + 50 - 62x\\ 36 - 60 x = 50 - 62 x\\ 2x = 50 - 36 = 14\\ x = 7 $$

So the sides are $3x-1=20$, $4x-7=21$ and hypotenuse $5x-6=29$.

A Pythagorean triple where all integers, but not one of the more familiar ones like (3,4,5) or (5,12,13)