x+12/100x=896

Solution for x+12/100x=896 equation:

x+12/100x=896

We move all terms to the left:

x+12/100x-(896)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-896*100x+12=0

Wy multiply elements

100x^2-89600x+12=0

a = 100; b = -89600; c = +12;
Δ = b2-4ac
Δ = -896002-4·100·12
Δ = 8028155200
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:

$\sqrt{\Delta}=\sqrt{8028155200}=\sqrt{1600*5017597}=\sqrt{1600}*\sqrt{5017597}=40\sqrt{5017597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89600)-40\sqrt{5017597}}{2*100}=\frac{89600-40\sqrt{5017597}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89600)+40\sqrt{5017597}}{2*100}=\frac{89600+40\sqrt{5017597}}{200}
$