What's 1 over 4x squared - 4x - 7= -7 when you're solving for x?

1 / (4x² - 4x - 7) = -7

-7(4x² - 4x - 7) = 1

-28x² + 28x + 49 = 1

28x² - 28x - 48 = 0

7x² - 7x - 12 = 0

x = [7 ± √(7² + 4*7*12)] / (2*7)

x = (7 + √385)/14 or x = (7 - √385)/14

(0.397, 0)

Is that:

1 / (4x² - 4x - 7) = -7

If so, let's start this out by getting the reciprocal of both sides:

4x² - 4x - 7 = -1/7

Now get in standard form:

4x² - 4x - 49/7 + 1/7 = 0
4x² - 4x - 48/7 = 0

Dividing both sides by 4:

x² - x - 12/7 = 0

x = [ -b ± √(b² - 4ac)] / (2a)
x = [ -(-1) ± √((-1)² - 4*1*(-12/7))] / (2*1)
x = [ 1 ± √(1 + 48/7)] / 2
x = [ 1 ± √(7/7 + 48/7)] / 2
x = [ 1 ± √(55/7)] / 2

x = 1/2 ± √(55/7) / 2
x = 1/2 ± √(55/7) * 1/2
x = 1/2 ± √(385)/7 * 1/2
x = 1/2 ± √(385) / 14

(1/4 • 1/4) - 4x - 7 = -7
1/8-4x-7=-7
1/8-4x=0
1/8=4x
1/32=x