435-x=x^2

Solution for 435-x=x^2 equation:

435-x=x^2

We move all terms to the left:

435-x-(x^2)=0

determiningTheFunctionDomain
-x^2-x+435=0

We add all the numbers together, and all the variables

-1x^2-1x+435=0

a = -1; b = -1; c = +435;
Δ = b2-4ac
Δ = -12-4·(-1)·435
Δ = 1741
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{-(-1)-\sqrt{1741}}{2*-1}=\frac{1-\sqrt{1741}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1741}}{2*-1}=\frac{1+\sqrt{1741}}{-2}
$