(25/x)+16x-(30/x)=0

Solution for (25/x)+16x-(30/x)=0 equation:

(25/x)+16x-(30/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+25/x)+16x-(+30/x)=0

We add all the numbers together, and all the variables

16x+(+25/x)-(+30/x)=0

We get rid of parentheses

16x+25/x-30/x=0

We multiply all the terms by the denominator


16x*x+25-30=0

We add all the numbers together, and all the variables

16x*x-5=0

Wy multiply elements

16x^2-5=0

a = 16; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·16·(-5)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*16}=\frac{0-8\sqrt{5}}{32}
=-\frac{8\sqrt{5}}{32}
=-\frac{\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*16}=\frac{0+8\sqrt{5}}{32}
=\frac{8\sqrt{5}}{32}
=\frac{\sqrt{5}}{4}
$