2x+2/5x+x=102,000

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

2x+2/5x+x=102.000

We move all terms to the left:

2x+2/5x+x-(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

2x+2/5x+x-102=0

We add all the numbers together, and all the variables

3x+2/5x-102=0

We multiply all the terms by the denominator


3x*5x-102*5x+2=0

Wy multiply elements

15x^2-510x+2=0

a = 15; b = -510; c = +2;
Δ = b2-4ac
Δ = -5102-4·15·2
Δ = 259980
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:

$\sqrt{\Delta}=\sqrt{259980}=\sqrt{4*64995}=\sqrt{4}*\sqrt{64995}=2\sqrt{64995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-2\sqrt{64995}}{2*15}=\frac{510-2\sqrt{64995}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+2\sqrt{64995}}{2*15}=\frac{510+2\sqrt{64995}}{30}
$