(x-3)(14000/x+1500)=14000

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Solution for (x-3)(14000/x+1500)=14000 equation: 



(x-3)(14000/x+1500)=14000

We move all terms to the left:

(x-3)(14000/x+1500)-(14000)=0



Domain of the equation: x+1500)!=0

x∈R



We multiply parentheses ..

(+14000x^2+1500x-42000x-4500)-14000=0

We get rid of parentheses

14000x^2+1500x-42000x-4500-14000=0

We add all the numbers together, and all the variables

14000x^2-40500x-18500=0

a = 14000; b = -40500; c = -18500;
Δ = b2-4ac
Δ = -405002-4·14000·(-18500)
Δ = 2676250000
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:


$\sqrt{\Delta}=\sqrt{2676250000}=\sqrt{250000*10705}=\sqrt{250000}*\sqrt{10705}=500\sqrt{10705}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40500)-500\sqrt{10705}}{2*14000}=\frac{40500-500\sqrt{10705}}{28000}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40500)+500\sqrt{10705}}{2*14000}=\frac{40500+500\sqrt{10705}}{28000}
$

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