Solve the following equations by using formula:

4x² - 4ax + (a² - b²) = 0

The given equation is 4x² - 4ax + (a² - b²) = 0.

Comparing it with ax² + bx + c = 0, we get
a = 4 , b = -4a , c = a² - b²

By using formula,

$x = \dfrac{-b ± \sqrt{b^2 - 4ac}}{2a}$

we obtain:

$\Rightarrow \dfrac{-(-4a) ± \sqrt{(-4a)^2 - 4 \times 4 \times (a^2 - b^2)}}{2 \times 4} \\[1em] \Rightarrow \dfrac{4a ± \sqrt{16a^2 - 16(a^2 - b^2)}}{8} \\[1em] \Rightarrow \dfrac{4a ± \sqrt{16a^2 - 16a^2 + 16b^2}}{8} \\[1em] \Rightarrow \dfrac{4a ± \sqrt{16b^2}}{8} \\[1em] \Rightarrow \dfrac{4a ± 4b}{8} \\[1em] \Rightarrow \dfrac{4a + 4b}{8} \text{ or } \dfrac{4a - 4b}{8} \\[1em] \Rightarrow \dfrac{a + b}{2} \text{ or } \dfrac{a - b}{2} \\[1em]$

Hence roots of the given equations are $\dfrac{a + b}{2} , \dfrac{a - b}{2}$.