(720/x-6)(x+4)=720

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Solution for (720/x-6)(x+4)=720 equation: 



(720/x-6)(x+4)=720

We move all terms to the left:

(720/x-6)(x+4)-(720)=0



Domain of the equation: x-6)(x+4)!=0

x∈R



We multiply parentheses ..

(+720x^2+2880x-6x-24)-720=0

We get rid of parentheses

720x^2+2880x-6x-24-720=0

We add all the numbers together, and all the variables

720x^2+2874x-744=0

a = 720; b = 2874; c = -744;
Δ = b2-4ac
Δ = 28742-4·720·(-744)
Δ = 10402596
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:


$\sqrt{\Delta}=\sqrt{10402596}=\sqrt{36*288961}=\sqrt{36}*\sqrt{288961}=6\sqrt{288961}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2874)-6\sqrt{288961}}{2*720}=\frac{-2874-6\sqrt{288961}}{1440}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2874)+6\sqrt{288961}}{2*720}=\frac{-2874+6\sqrt{288961}}{1440}
$

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