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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-13x^2+11x+247x-209=0

We add all the numbers together, and all the variables

-13x^2+258x-209=0

a = -13; b = 258; c = -209;
Δ = b2-4ac
Δ = 2582-4·(-13)·(-209)
Δ = 55696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55696}=236$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(258)-236}{2*-13}=\frac{-494}{-26}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(258)+236}{2*-13}=\frac{-22}{-26}
=11/13
$