Question
$$(2x-3)^2-15 = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 15 }}{ 2 } & x_2 = \dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 15 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (2x-3)^2-15 &= 0&& \text{simplify left side} \\[1 em]4x^2-12x+9-15 &= 0&& \\[1 em]4x^2-12x-6 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-12x-6 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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