26x+24/x=-60

Solution for 26x+24/x=-60 equation:

26x+24/x=-60

We move all terms to the left:

26x+24/x-(-60)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

26x+24/x+60=0

We multiply all the terms by the denominator


26x*x+60*x+24=0

We add all the numbers together, and all the variables

60x+26x*x+24=0

Wy multiply elements

26x^2+60x+24=0

a = 26; b = 60; c = +24;
Δ = b2-4ac
Δ = 602-4·26·24
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{69}}{2*26}=\frac{-60-4\sqrt{69}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{69}}{2*26}=\frac{-60+4\sqrt{69}}{52}
$