14,000+160x=24,000+200/x

Solution for 14,000+160x=24,000+200/x equation:

14.000+160x=24.000+200/x

We move all terms to the left:

14.000+160x-(24.000+200/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

160x-(200/x+24)+14.000=0

We add all the numbers together, and all the variables

160x-(200/x+24)+14=0

We get rid of parentheses

160x-200/x-24+14=0

We multiply all the terms by the denominator


160x*x-24*x+14*x-200=0

We add all the numbers together, and all the variables

-10x+160x*x-200=0

Wy multiply elements

160x^2-10x-200=0

a = 160; b = -10; c = -200;
Δ = b2-4ac
Δ = -102-4·160·(-200)
Δ = 128100
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:

$\sqrt{\Delta}=\sqrt{128100}=\sqrt{100*1281}=\sqrt{100}*\sqrt{1281}=10\sqrt{1281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{1281}}{2*160}=\frac{10-10\sqrt{1281}}{320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{1281}}{2*160}=\frac{10+10\sqrt{1281}}{320}
$