x^2-14x+33=65

Solution for x^2-14x+33=65 equation:

x^2-14x+33=65

We move all terms to the left:

x^2-14x+33-(65)=0

We add all the numbers together, and all the variables

x^2-14x-32=0

a = 1; b = -14; c = -32;
Δ = b2-4ac
Δ = -142-4·1·(-32)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-18}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+18}{2*1}=\frac{32}{2}
=16
$