0=23-14x-x^2

Solution for 0=23-14x-x^2 equation:

0=23-14x-x^2

We move all terms to the left:

0-(23-14x-x^2)=0

We add all the numbers together, and all the variables

-(23-14x-x^2)=0

We get rid of parentheses

x^2+14x-23=0

a = 1; b = 14; c = -23;
Δ = b2-4ac
Δ = 142-4·1·(-23)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-12\sqrt{2}}{2*1}=\frac{-14-12\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+12\sqrt{2}}{2*1}=\frac{-14+12\sqrt{2}}{2}
$