2x+6/12x=15000

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Solution for 2x+6/12x=15000 equation: 



2x+6/12x=15000

We move all terms to the left:

2x+6/12x-(15000)=0



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



We multiply all the terms by the denominator


2x*12x-15000*12x+6=0

Wy multiply elements

24x^2-180000x+6=0

a = 24; b = -180000; c = +6;
Δ = b2-4ac
Δ = -1800002-4·24·6
Δ = 32399999424
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:


$\sqrt{\Delta}=\sqrt{32399999424}=\sqrt{576*56249999}=\sqrt{576}*\sqrt{56249999}=24\sqrt{56249999}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180000)-24\sqrt{56249999}}{2*24}=\frac{180000-24\sqrt{56249999}}{48}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180000)+24\sqrt{56249999}}{2*24}=\frac{180000+24\sqrt{56249999}}{48}
$

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