x+(1/50x)=300

Solution for x+(1/50x)=300 equation:

x+(1/50x)=300

We move all terms to the left:

x+(1/50x)-(300)=0


Domain of the equation: 50x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/50x)-300=0

We get rid of parentheses

x+1/50x-300=0

We multiply all the terms by the denominator


x*50x-300*50x+1=0

Wy multiply elements

50x^2-15000x+1=0

a = 50; b = -15000; c = +1;
Δ = b2-4ac
Δ = -150002-4·50·1
Δ = 224999800
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:

$\sqrt{\Delta}=\sqrt{224999800}=\sqrt{100*2249998}=\sqrt{100}*\sqrt{2249998}=10\sqrt{2249998}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15000)-10\sqrt{2249998}}{2*50}=\frac{15000-10\sqrt{2249998}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15000)+10\sqrt{2249998}}{2*50}=\frac{15000+10\sqrt{2249998}}{100}
$