44/100x=X-42

Solution for 44/100x=X-42 equation:

44/100x=x-42

We move all terms to the left:

44/100x-(x-42)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We get rid of parentheses

44/100x-x+42=0

We multiply all the terms by the denominator


-x*100x+42*100x+44=0

Wy multiply elements

-100x^2+4200x+44=0

a = -100; b = 4200; c = +44;
Δ = b2-4ac
Δ = 42002-4·(-100)·44
Δ = 17657600
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:

$\sqrt{\Delta}=\sqrt{17657600}=\sqrt{6400*2759}=\sqrt{6400}*\sqrt{2759}=80\sqrt{2759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4200)-80\sqrt{2759}}{2*-100}=\frac{-4200-80\sqrt{2759}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4200)+80\sqrt{2759}}{2*-100}=\frac{-4200+80\sqrt{2759}}{-200}
$