Explanation:
Pythagoras :
c² = a² + b²
the only problem : we don't know which one of the 3 expressions is the longest side (= c = Hypotenuse).
let's try with 8x -21
(8x - 21)² = (3x - 7)² + (6x)²
64x² - 336x + 441 = 9x² - 42x + 49 + 36x²
19x² - 294x + 392 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 19
b = -294
c = 392
x = (294 ± sqrt(86436 - 4×19×392))/(2×19) =
= (294 ± sqrt(56644))/38 =
= (294 ± 238)/38
x1 = (294 + 238)/38 = 532/38 = 14
x2 = (294 - 238)/38 = 56/38 = 28/19 = 1.473684211...
I assume, we are looking for a whole number solution.
so, x = 14 is the solution.