Question

7x + 1 = 6x²

Answer 1

Given: 7x + 1 = 6x²
Rewriting this equation in the standard form of the quadratic equation, we get:
6x² – 7x – 1 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 6, b = –7 and c = –1
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 6, b = –7 and c = –1, we get:
$$\begin{gathered} x=\frac{-\left(-7\right)\pm \sqrt{{\left(-7\right)}^2-4\times 6\times \left(-1\right)}}{2\times 6} \\ =\frac{7\pm \sqrt{49+24}}{12} \\ =\frac{7\pm \sqrt{73}}{12} \end{gathered}$$
Thus, the solution of the given quadratic equation is x = $\frac{7+\sqrt{73}}{12},\frac{7-\sqrt{73}}{12}$.