((60/x)+2,5)*(x-4)=60

Solution for ((60/x)+2,5)*(x-4)=60 equation:

((60/x)+2.5)(x-4)=60

We move all terms to the left:

((60/x)+2.5)(x-4)-(60)=0


Domain of the equation: x)+2.5)(x-4)!=0

x∈R


We add all the numbers together, and all the variables

((+60/x)+2.5)(x-4)-60=0

We multiply all the terms by the denominator


((+60-60*x)+2.5)(x-4)=0


We calculate terms in parentheses: +((+60-60*x)+2.5)(x-4), so:

(+60-60*x)+2.5)(x-4

We add all the numbers together, and all the variables

(-60x+60)+2.5)(x-4

We get rid of parentheses

-60x+2.5)(x+60-4

We add all the numbers together, and all the variables

-60x+2.5)(x+56

Back to the equation:

+(-60x+2.5)(x+56)


We multiply parentheses ..

(-60x^2-3360x+2.5x+140)=0

We get rid of parentheses

-60x^2-3360x+2.5x+140=0

We add all the numbers together, and all the variables

-60x^2-3357.5x+140=0

a = -60; b = -3357.5; c = +140;
Δ = b2-4ac
Δ = -3357.52-4·(-60)·140
Δ = 11306406.25
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{-(-3357.5)-\sqrt{11306406.25}}{2*-60}=\frac{3357.5-\sqrt{11306406.25}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3357.5)+\sqrt{11306406.25}}{2*-60}=\frac{3357.5+\sqrt{11306406.25}}{-120}
$