19/19.x+110=200-8x

Solution for 19/19.x+110=200-8x equation:

19/19.x+110=200-8x

We move all terms to the left:

19/19.x+110-(200-8x)=0


Domain of the equation: 19.x!=0

x!=0/19.

x!=0

x∈R


We add all the numbers together, and all the variables

19/19.x-(-8x+200)+110=0

We get rid of parentheses

19/19.x+8x-200+110=0

We multiply all the terms by the denominator


8x*19.x-200*19.x+110*19.x+19=0

Wy multiply elements

152x^2-3800x+2090x+19=0

We add all the numbers together, and all the variables

152x^2-1710x+19=0

a = 152; b = -1710; c = +19;
Δ = b2-4ac
Δ = -17102-4·152·19
Δ = 2912548
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:

$\sqrt{\Delta}=\sqrt{2912548}=\sqrt{1444*2017}=\sqrt{1444}*\sqrt{2017}=38\sqrt{2017}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1710)-38\sqrt{2017}}{2*152}=\frac{1710-38\sqrt{2017}}{304}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1710)+38\sqrt{2017}}{2*152}=\frac{1710+38\sqrt{2017}}{304}
$