(60/x-0.5)(x+4)=60

Solution for (60/x-0.5)(x+4)=60 equation:

(60/x-0.5)(x+4)=60

We move all terms to the left:

(60/x-0.5)(x+4)-(60)=0


Domain of the equation: x-0.5)(x+4)!=0

x∈R


We multiply parentheses ..

(+60x^2+240x-0.5x-2)-60=0

We get rid of parentheses

60x^2+240x-0.5x-2-60=0

We add all the numbers together, and all the variables

60x^2+239.5x-62=0

a = 60; b = 239.5; c = -62;
Δ = b2-4ac
Δ = 239.52-4·60·(-62)
Δ = 72240.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(239.5)-\sqrt{72240.25}}{2*60}=\frac{-239.5-\sqrt{72240.25}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(239.5)+\sqrt{72240.25}}{2*60}=\frac{-239.5+\sqrt{72240.25}}{120}
$