First write cosh and sinh as exponentials, from their respective definitions:sinh x = 1/2 (ex - e-x)cosh x = 1/2 (ex + e-x)So: 3 * 1/2 (ex + e-x) - 4 * 1/2 (ex - e-x) = 7Multiply by 2: 3 * (ex + e-x) - 4 * (ex - e-x) = 14Expanding gives: 3 * ex + 3 * e-x - 4 * ex + 4 * e-x = 14Collecting terms: -ex + 7 * e-x = 14So: ex - 7 * e-x + 14 = 0Since ex is not 0, we can multiply by it:ex * ex - 7 * e-x *ex + 14 * ex = 0e2x - 7 + 14 * ex = 0This is a quadratic in ex, and we can use the quadratic formula to obtain:ex = -7 +- 2 root 14But ex > 0, so we discount the negative root:ex = -7 + 2 root 14x = ln ( -7 + 2 root 14)Which can easily be checked with a calculator.