Question

How do you factor `2x=6x^{2}-7`?

Answer 1

see link in Explanation
the quadratic formula is `x=(-b\pm\sqrt{b^2-4ac})/(2a)`

Explanation:

`2x=6x^2-7`
make it a quadratic: `0=6x^2-2x-7`
apply quadratic formula (click the link).

Answer 2

Since `a!=1` you need to multiply a and c together before factoring.
Now you need something that multiplies to be `-42` (`6*-7`)and has a sum of `2`. There are no integers which allows this to work, so this quadratic equation is unfactorable. In such case, you need to use the formula, graph it, or use other methods such as completing the square.