(240/x+3)(x-4)=240

Solution for (240/x+3)(x-4)=240 equation:

(240/x+3)(x-4)=240

We move all terms to the left:

(240/x+3)(x-4)-(240)=0


Domain of the equation: x+3)(x-4)!=0

x∈R


We multiply parentheses ..

(+240x^2-960x+3x-12)-240=0

We get rid of parentheses

240x^2-960x+3x-12-240=0

We add all the numbers together, and all the variables

240x^2-957x-252=0

a = 240; b = -957; c = -252;
Δ = b2-4ac
Δ = -9572-4·240·(-252)
Δ = 1157769
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:

$\sqrt{\Delta}=\sqrt{1157769}=\sqrt{9*128641}=\sqrt{9}*\sqrt{128641}=3\sqrt{128641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-957)-3\sqrt{128641}}{2*240}=\frac{957-3\sqrt{128641}}{480}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-957)+3\sqrt{128641}}{2*240}=\frac{957+3\sqrt{128641}}{480}
$