2500/x+2500/2x=41

Solution for 2500/x+2500/2x=41 equation:

2500/x+2500/2x=41

We move all terms to the left:

2500/x+2500/2x-(41)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


5000x/2x^2+2500x/2x^2-41=0

We multiply all the terms by the denominator


5000x+2500x-41*2x^2=0

We add all the numbers together, and all the variables

7500x-41*2x^2=0

Wy multiply elements

-82x^2+7500x=0

a = -82; b = 7500; c = 0;
Δ = b2-4ac
Δ = 75002-4·(-82)·0
Δ = 56250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56250000}=7500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7500)-7500}{2*-82}=\frac{-15000}{-164}
=91+19/41
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7500)+7500}{2*-82}=\frac{0}{-164}
=0
$