Question
$$4a^2-5a+7 = 6a^2+3a-2$$
Answer
$$ \begin{matrix}a_1 = -2-\dfrac{\sqrt{ 34 }}{ 2 } & a_2 = -2+\dfrac{\sqrt{ 34 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4a^2-5a+7 &= 6a^2+3a-2&& \text{move all terms to the left hand side } \\[1 em]4a^2-5a+7-6a^2-3a+2 &= 0&& \text{simplify left side} \\[1 em]-2a^2-8a+9 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}-8x+9 = 0 $ is a quadratic equation.
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