2,50x+50=2,5+50/x

Solution for 2,50x+50=2,5+50/x equation:

2.50x+50=2.5+50/x

We move all terms to the left:

2.50x+50-(2.5+50/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

2.50x-(50/x+2.5)+50=0

We get rid of parentheses

2.50x-50/x-2.5+50=0

We multiply all the terms by the denominator


(2.50x)*x-(2.5)*x+50*x-50=0

We add all the numbers together, and all the variables

(+2.50x)*x-(2.5)*x+50*x-50=0

We add all the numbers together, and all the variables

50x+(+2.50x)*x-(2.5)*x-50=0

We multiply parentheses

2x^2+50x-2.5x-50=0

We add all the numbers together, and all the variables

2x^2+47.5x-50=0

a = 2; b = 47.5; c = -50;
Δ = b2-4ac
Δ = 47.52-4·2·(-50)
Δ = 2656.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47.5)-\sqrt{2656.25}}{2*2}=\frac{-47.5-\sqrt{2656.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47.5)+\sqrt{2656.25}}{2*2}=\frac{-47.5+\sqrt{2656.25}}{4}
$