1/16x^-2=x+15

Solution for 1/16x^-2=x+15 equation:

1/16x^-2=x+15

We move all terms to the left:

1/16x^-2-(x+15)=0


Domain of the equation: 16x^!=0

x!=0/16

x!=0

x∈R


We get rid of parentheses

1/16x^-x-15-2=0

We multiply all the terms by the denominator


-x*16x^-15*16x^-2*16x^+1=0

Wy multiply elements

-16x^2-240x-32x+1=0

We add all the numbers together, and all the variables

-16x^2-272x+1=0

a = -16; b = -272; c = +1;
Δ = b2-4ac
Δ = -2722-4·(-16)·1
Δ = 74048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{74048}=\sqrt{64*1157}=\sqrt{64}*\sqrt{1157}=8\sqrt{1157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-8\sqrt{1157}}{2*-16}=\frac{272-8\sqrt{1157}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+8\sqrt{1157}}{2*-16}=\frac{272+8\sqrt{1157}}{-32}
$