5x+1/x-64=0

Solution for 5x+1/x-64=0 equation:

5x+1/x-64=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-64*x+1=0

We add all the numbers together, and all the variables

-64x+5x*x+1=0

Wy multiply elements

5x^2-64x+1=0

a = 5; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·5·1
Δ = 4076
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:

$\sqrt{\Delta}=\sqrt{4076}=\sqrt{4*1019}=\sqrt{4}*\sqrt{1019}=2\sqrt{1019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{1019}}{2*5}=\frac{64-2\sqrt{1019}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{1019}}{2*5}=\frac{64+2\sqrt{1019}}{10}
$