x=1.1x^2-418x+50,459

Solution for x=1.1x^2-418x+50,459 equation:

x=1.1x^2-418x+50.459

We move all terms to the left:

x-(1.1x^2-418x+50.459)=0

We get rid of parentheses

-1.1x^2+x+418x-50.459=0

We add all the numbers together, and all the variables

-1.1x^2+419x-50.459=0

a = -1.1; b = 419; c = -50.459;
Δ = b2-4ac
Δ = 4192-4·(-1.1)·(-50.459)
Δ = 175338.9804
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{-(419)-\sqrt{175338.9804}}{2*-1.1}=\frac{-419-\sqrt{175338.9804}}{-2.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(419)+\sqrt{175338.9804}}{2*-1.1}=\frac{-419+\sqrt{175338.9804}}{-2.2}
$