Question
$$4v^2+3v-(6v-7+7v^2) = 0$$
Answer
$$ \begin{matrix}v_1 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 93 }}{ 6 } & v_2 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 93 }}{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4v^2+3v-(6v-7+7v^2) &= 0&& \text{simplify left side} \\[1 em]4v^2+3v-6v+7-7v^2 &= 0&& \\[1 em]-3v^2-3v+7 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}-3x+7 = 0 $ is a quadratic equation.
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