0=105-16x-x^2

Solution for 0=105-16x-x^2 equation:

0=105-16x-x^2

We move all terms to the left:

0-(105-16x-x^2)=0

We add all the numbers together, and all the variables

-(105-16x-x^2)=0

We get rid of parentheses

x^2+16x-105=0

a = 1; b = 16; c = -105;
Δ = b2-4ac
Δ = 162-4·1·(-105)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-26}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+26}{2*1}=\frac{10}{2}
=5
$