23+2x-x^2=0

Solution for 23+2x-x^2=0 equation:

23+2x-x^2=0

We add all the numbers together, and all the variables

-1x^2+2x+23=0

a = -1; b = 2; c = +23;
Δ = b2-4ac
Δ = 22-4·(-1)·23
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{6}}{2*-1}=\frac{-2-4\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{6}}{2*-1}=\frac{-2+4\sqrt{6}}{-2}
$