59/x+x-1=15

Solution for 59/x+x-1=15 equation:

59/x+x-1=15

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+59/x-16=0

We multiply all the terms by the denominator


x*x-16*x+59=0

We add all the numbers together, and all the variables

-16x+x*x+59=0

Wy multiply elements

x^2-16x+59=0

a = 1; b = -16; c = +59;
Δ = b2-4ac
Δ = -162-4·1·59
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{5}}{2*1}=\frac{16-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{5}}{2*1}=\frac{16+2\sqrt{5}}{2}
$