75/100x=x-12

Solution for 75/100x=x-12 equation:

75/100x=x-12

We move all terms to the left:

75/100x-(x-12)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We get rid of parentheses

75/100x-x+12=0

We multiply all the terms by the denominator


-x*100x+12*100x+75=0

Wy multiply elements

-100x^2+1200x+75=0

a = -100; b = 1200; c = +75;
Δ = b2-4ac
Δ = 12002-4·(-100)·75
Δ = 1470000
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:

$\sqrt{\Delta}=\sqrt{1470000}=\sqrt{490000*3}=\sqrt{490000}*\sqrt{3}=700\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-700\sqrt{3}}{2*-100}=\frac{-1200-700\sqrt{3}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+700\sqrt{3}}{2*-100}=\frac{-1200+700\sqrt{3}}{-200}
$