Solving equation?

Question

$6x^2+x= 40$

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Answer 1 · 2017-12-02T21:38:14

$2$ real solutions:

$x=2.5\quad,\quad x=-2.\overline{6}$

Let’s first rearrange the equation:

$6x^2+x-40=0$

It’s a quadratic equation, which we can use the quadratic equation to solve.

Since the equation is in standard form, let’s define the variables:

We can now plug those values into the quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies x=\frac{-1\pm\sqrt{(1)^2-4(6)(-40)}}{2(6)}$

$\implies x=\frac{-1\pm\sqrt{1+960}}{12}$

$\implies x=\frac{-1\pm 31}{12}$

$\implies x=2.5\quad,\quad x=-2.\overline{6}$