(x+10)(2400/x-8)=2400

Solution for (x+10)(2400/x-8)=2400 equation:

(x+10)(2400/x-8)=2400

We move all terms to the left:

(x+10)(2400/x-8)-(2400)=0


Domain of the equation: x-8)!=0

x∈R


We multiply parentheses ..

(+2400x^2-8x+24000x-80)-2400=0

We get rid of parentheses

2400x^2-8x+24000x-80-2400=0

We add all the numbers together, and all the variables

2400x^2+23992x-2480=0

a = 2400; b = 23992; c = -2480;
Δ = b2-4ac
Δ = 239922-4·2400·(-2480)
Δ = 599424064
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:

$\sqrt{\Delta}=\sqrt{599424064}=\sqrt{64*9366001}=\sqrt{64}*\sqrt{9366001}=8\sqrt{9366001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23992)-8\sqrt{9366001}}{2*2400}=\frac{-23992-8\sqrt{9366001}}{4800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23992)+8\sqrt{9366001}}{2*2400}=\frac{-23992+8\sqrt{9366001}}{4800}
$