19/44x=x-850

Solution for 19/44x=x-850 equation:

19/44x=x-850

We move all terms to the left:

19/44x-(x-850)=0


Domain of the equation: 44x!=0

x!=0/44

x!=0

x∈R


We get rid of parentheses

19/44x-x+850=0

We multiply all the terms by the denominator


-x*44x+850*44x+19=0

Wy multiply elements

-44x^2+37400x+19=0

a = -44; b = 37400; c = +19;
Δ = b2-4ac
Δ = 374002-4·(-44)·19
Δ = 1398763344
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:

$\sqrt{\Delta}=\sqrt{1398763344}=\sqrt{16*87422709}=\sqrt{16}*\sqrt{87422709}=4\sqrt{87422709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37400)-4\sqrt{87422709}}{2*-44}=\frac{-37400-4\sqrt{87422709}}{-88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37400)+4\sqrt{87422709}}{2*-44}=\frac{-37400+4\sqrt{87422709}}{-88}
$