x=x^2-14x+44

Solution for x=x^2-14x+44 equation:

x=x^2-14x+44

We move all terms to the left:

x-(x^2-14x+44)=0

We get rid of parentheses

-x^2+x+14x-44=0

We add all the numbers together, and all the variables

-1x^2+15x-44=0

a = -1; b = 15; c = -44;
Δ = b2-4ac
Δ = 152-4·(-1)·(-44)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-7}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+7}{2*-1}=\frac{-8}{-2}
=+4
$