7/x-16x=0

Solution for 7/x-16x=0 equation:

7/x-16x=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-16x+7/x=0

We multiply all the terms by the denominator


-16x*x+7=0

Wy multiply elements

-16x^2+7=0

a = -16; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-16)·7
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*-16}=\frac{0-8\sqrt{7}}{-32}
=-\frac{8\sqrt{7}}{-32}
=-\frac{\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*-16}=\frac{0+8\sqrt{7}}{-32}
=\frac{8\sqrt{7}}{-32}
=\frac{\sqrt{7}}{-4}
$