(19-x)11x+13=209

Solution for (19-x)11x+13=209 equation:

(19-x)11x+13=209

We move all terms to the left:

(19-x)11x+13-(209)=0

We add all the numbers together, and all the variables

(-1x+19)11x+13-209=0

We add all the numbers together, and all the variables

(-1x+19)11x-196=0

We multiply parentheses

-11x^2+209x-196=0

a = -11; b = 209; c = -196;
Δ = b2-4ac
Δ = 2092-4·(-11)·(-196)
Δ = 35057
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(209)-\sqrt{35057}}{2*-11}=\frac{-209-\sqrt{35057}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(209)+\sqrt{35057}}{2*-11}=\frac{-209+\sqrt{35057}}{-22}
$