6x+2/5x=102,000

Solution for 6x+2/5x=102,000 equation:

6x+2/5x=102.000

We move all terms to the left:

6x+2/5x-(102.000)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

6x+2/5x-102=0

We multiply all the terms by the denominator


6x*5x-102*5x+2=0

Wy multiply elements

30x^2-510x+2=0

a = 30; b = -510; c = +2;
Δ = b2-4ac
Δ = -5102-4·30·2
Δ = 259860
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:

$\sqrt{\Delta}=\sqrt{259860}=\sqrt{4*64965}=\sqrt{4}*\sqrt{64965}=2\sqrt{64965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-2\sqrt{64965}}{2*30}=\frac{510-2\sqrt{64965}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+2\sqrt{64965}}{2*30}=\frac{510+2\sqrt{64965}}{60}
$