Chapter 10 - Systems of Equations and Inequalities - Section 10.6 Systems of Nonlinear Equations - 10.6 Assess Your Understanding - Page 797: 102

$\frac{-3\pm\sqrt {65}}{7}$

Given $7x^2=8-6x$ or $7x^2+6x-8-0$, use the quadratic formula, we can identify $a=7, b=6, c=-8$, thus: $x=\frac{-b\pm\sqrt {b^2-4ac}}{2a} =\frac{-6\pm\sqrt {6^2-4(7)(-8)}}{2(7)} =\frac{-3\pm\sqrt {3^2-(7)(-8)}}{7} =\frac{-3\pm\sqrt {65}}{7}$