x+30/x=2600

Solution for x+30/x=2600 equation:

x+30/x=2600

We move all terms to the left:

x+30/x-(2600)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-2600*x+30=0

We add all the numbers together, and all the variables

-2600x+x*x+30=0

Wy multiply elements

x^2-2600x+30=0

a = 1; b = -2600; c = +30;
Δ = b2-4ac
Δ = -26002-4·1·30
Δ = 6759880
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:

$\sqrt{\Delta}=\sqrt{6759880}=\sqrt{4*1689970}=\sqrt{4}*\sqrt{1689970}=2\sqrt{1689970}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2600)-2\sqrt{1689970}}{2*1}=\frac{2600-2\sqrt{1689970}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2600)+2\sqrt{1689970}}{2*1}=\frac{2600+2\sqrt{1689970}}{2}
$