43-2x=x^2

Solution for 43-2x=x^2 equation:

43-2x=x^2

We move all terms to the left:

43-2x-(x^2)=0

determiningTheFunctionDomain
-x^2-2x+43=0

We add all the numbers together, and all the variables

-1x^2-2x+43=0

a = -1; b = -2; c = +43;
Δ = b2-4ac
Δ = -22-4·(-1)·43
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{11}}{2*-1}=\frac{2-4\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{11}}{2*-1}=\frac{2+4\sqrt{11}}{-2}
$