x^2-14x+33=240

Solution for x^2-14x+33=240 equation:

x^2-14x+33=240

We move all terms to the left:

x^2-14x+33-(240)=0

We add all the numbers together, and all the variables

x^2-14x-207=0

a = 1; b = -14; c = -207;
Δ = b2-4ac
Δ = -142-4·1·(-207)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-32}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+32}{2*1}=\frac{46}{2}
=23
$