5x-1=1/x+15

Solution for 5x-1=1/x+15 equation:

5x-1=1/x+15

We move all terms to the left:

5x-1-(1/x+15)=0


Domain of the equation: x+15)!=0

x∈R


We get rid of parentheses

5x-1/x-15-1=0

We multiply all the terms by the denominator


5x*x-15*x-1*x-1=0

We add all the numbers together, and all the variables

-16x+5x*x-1=0

Wy multiply elements

5x^2-16x-1=0

a = 5; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·5·(-1)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{69}}{2*5}=\frac{16-2\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{69}}{2*5}=\frac{16+2\sqrt{69}}{10}
$