What are the two roots for this quadratic?

Question

45.3 = ((2x)^2) / (0.526-x)(1.46-x)

Answer 1

45.3 = [(2x)^2] / [(0.526 - x)(1.46 - x)]

Multiply both sides by (0.56 - x)(1.46 - x) :
45.3(0.56 - x)(1.46 - x) = 4x^2

Multiply out the LHS and sum like terms :
37.03728 - 91.506x + 45.3x^2 = 4x^2

Subtract 4x^2 from both sides and rearrange :
41.3x^2 - 91.506x + 37.03728 = 0

Using the quadratic formula :
x = {91.506 ± sqrt[(-91.506)^2 - (4)(41.3)(37.03728)]} / (2 * 41.3)

= [91.506 ± sqrt(2254.78938)] / 82.6

= 0.533 or 1.683

Answer 2

To figure this out, write 45.3(.526-x)(1.46-x) - 2x^2 = 0
FOIL it out ...
45.3(.76796 - 1.986x + x^2) - 2x^2 = 0
Multiply out the 45.3 ...
34.788588 - 89.9658x + 45.3x^2 - 2x^2 = 0
combine the quad terms at the end and rearrange in standard form...
43.3x^2 - 89.9658x + 34.788588 = 0
Put this into the quadratic formula, but first check b^2 - 4ac to see if it has any real solutions...
b^2 - 4ac = 89.9658^2 - 4x43.3x34.788588 = 2868.461728
sqrt this ... approx 45.48034441
now put this in the quadratic formula. I'm going to round these to the nearest unit to make it easier to type in, when you work this out for yourself you can use the full approximations to get a better answer.
(90 +/- 46)/(2x43) = 136/86 or 44/86
Where in the world did you get these numbers from?!?! Are they decimial approximations of surds? If so, you'd be better to keep the surds and work with them, it would be more accurate, and probably easier also.
PS -- I see I goofed early on, wrote 2x^2 rather than (2x)^2. When you do it yourself, correct for this.
PS -- Your question, as stated, is not a quadratic, it is a rational equation. And it is undefined at the values x = .526 and x = 1.46. Could this be what you're looking for?

Answer 3

the same as the quot of it`s equal in sum