How the quadratic formula works:
For any quadratic equation ax² + bx + c = 0, the solution is
.
In the case of our equation 7x² - x = 7, first we need to subtract 7 from each side so that we have 0 on the right.
7x² - x - 7 = 0
Identify the values of a, b, and c.
a = 7, b = -1, and c = -7.
Plug these into our quadratic formula and solve.
![x=(-(-1)\pm√((-1)^2-4(7)(-7)))/(2(7))=\boxed{(1\pm√(197))/(14)]()
There are two values for x: (1+√197)/14 and (1-√197)/14.
The approximate values for these are 1.073976 and -0.931119.