Answer
$x = ±3$
Work Step by Step
1. Power equation
For example:
$7^{x} + 3 = 0$ is an exponential equation. (The variable is the exponent.)
$x^{7} + 3 =0 $ is a power equation. (The variable is raised to the power of a number.)
2. Solve
$5x^{6} + 20 = 3x^{6} + 1478$
$5x^{6} - 3x^{6} = 1478 -20$
$2x^{6} = 1458$
$x^{6} = 729$
$x = ±(729)^{\frac{1}{6}}$
$x = ±3$
Check:
When $x = 3$
$5(3)^{6} + 20 \overset{?}{=} 3(3)^{6} + 1478$
$5(729) + 20 \overset{?}{=} 3(729) + 1478$
$3645 + 20 \overset{?}{=} 2187 + 1478$
$3665 = 3665$
When $x = -3$
$5(-3)^{6} + 20 \overset{?}{=} 3(-3)^{6} + 1478$
$5(729) + 20 \overset{?}{=} 3(729) + 1478$
$3645 + 20 \overset{?}{=} 2187 + 1478$
$3665 = 3665$
