Identify the coefficients $a$, $b$, and $c$ in the quadratic equation $3x^2-4x+7=0$, given the standard form $a{x}^2+bx+c=0$.

Solve $2x^2+x-6=0$ by factoring.

Find two consecutive positive even integers whose squares sum to $340$.

A rectangular planter's length is three times its width. Its area is $192$ square meters. Find the width and length.

Use the quadratic formula to solve for: $(x+2)(x+5)-14=0$.