x+25/x=67000

Solution for x+25/x=67000 equation:

x+25/x=67000

We move all terms to the left:

x+25/x-(67000)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-67000*x+25=0

We add all the numbers together, and all the variables

-67000x+x*x+25=0

Wy multiply elements

x^2-67000x+25=0

a = 1; b = -67000; c = +25;
Δ = b2-4ac
Δ = -670002-4·1·25
Δ = 4488999900
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:

$\sqrt{\Delta}=\sqrt{4488999900}=\sqrt{100*44889999}=\sqrt{100}*\sqrt{44889999}=10\sqrt{44889999}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67000)-10\sqrt{44889999}}{2*1}=\frac{67000-10\sqrt{44889999}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67000)+10\sqrt{44889999}}{2*1}=\frac{67000+10\sqrt{44889999}}{2}
$