0.05x+25+(125/x)=0

Solution for 0.05x+25+(125/x)=0 equation:

0.05x+25+(125/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

0.05x+(+125/x)+25=0

We get rid of parentheses

0.05x+125/x+25=0

We multiply all the terms by the denominator


(0.05x)*x+25*x+125=0

We add all the numbers together, and all the variables

(+0.05x)*x+25*x+125=0

We add all the numbers together, and all the variables

25x+(+0.05x)*x+125=0

We multiply parentheses

0x^2+25x+125=0

We add all the numbers together, and all the variables

x^2+25x+125=0

a = 1; b = 25; c = +125;
Δ = b2-4ac
Δ = 252-4·1·125
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{5}}{2*1}=\frac{-25-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{5}}{2*1}=\frac{-25+5\sqrt{5}}{2}
$