As follows:
\(2x^2+5x+12=19-7x\rightarrow 2x^2+12x-7=0\\ \text{ use the quadratic formula to find x } x= \frac{-12\pm \sqrt{12^2+4\times 2\times 7}}{2\times2}\\ x = \frac{-12\pm\sqrt{200}}{4}\\ \text{ positive difference: }\sqrt{200}/2\rightarrow 5\sqrt2\)
