# How do you solve for x in a^2x+b^2x+7=3c?

Isolate all terms with $x$ on one side of the equation.
${a}^{2} x + {b}^{2} x = 3 c - 7$
$x \left({a}^{2} + {b}^{2}\right) = 3 c - 7$
$x = \frac{3 c - 7}{{a}^{2} + {b}^{2}}$