x+12/100x=300

Solution for x+12/100x=300 equation:

x+12/100x=300

We move all terms to the left:

x+12/100x-(300)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-300*100x+12=0

Wy multiply elements

100x^2-30000x+12=0

a = 100; b = -30000; c = +12;
Δ = b2-4ac
Δ = -300002-4·100·12
Δ = 899995200
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:

$\sqrt{\Delta}=\sqrt{899995200}=\sqrt{1600*562497}=\sqrt{1600}*\sqrt{562497}=40\sqrt{562497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30000)-40\sqrt{562497}}{2*100}=\frac{30000-40\sqrt{562497}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30000)+40\sqrt{562497}}{2*100}=\frac{30000+40\sqrt{562497}}{200}
$