-x^2-32=14x+1

Solution for -x^2-32=14x+1 equation:

-x^2-32=14x+1

We move all terms to the left:

-x^2-32-(14x+1)=0

We add all the numbers together, and all the variables

-1x^2-(14x+1)-32=0

We get rid of parentheses

-1x^2-14x-1-32=0

We add all the numbers together, and all the variables

-1x^2-14x-33=0

a = -1; b = -14; c = -33;
Δ = b2-4ac
Δ = -142-4·(-1)·(-33)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8}{2*-1}=\frac{6}{-2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8}{2*-1}=\frac{22}{-2}
=-11
$