(7/100x)+x=50

Solution for (7/100x)+x=50 equation:

(7/100x)+x=50

We move all terms to the left:

(7/100x)+x-(50)=0


Domain of the equation: 100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7/100x)+x-50=0

We add all the numbers together, and all the variables

x+(+7/100x)-50=0

We get rid of parentheses

x+7/100x-50=0

We multiply all the terms by the denominator


x*100x-50*100x+7=0

Wy multiply elements

100x^2-5000x+7=0

a = 100; b = -5000; c = +7;
Δ = b2-4ac
Δ = -50002-4·100·7
Δ = 24997200
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:

$\sqrt{\Delta}=\sqrt{24997200}=\sqrt{400*62493}=\sqrt{400}*\sqrt{62493}=20\sqrt{62493}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-20\sqrt{62493}}{2*100}=\frac{5000-20\sqrt{62493}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+20\sqrt{62493}}{2*100}=\frac{5000+20\sqrt{62493}}{200}
$