(x-2)(x-14)-45=0

Solution for (x-2)(x-14)-45=0 equation:

(x-2)(x-14)-45=0

We multiply parentheses ..

(+x^2-14x-2x+28)-45=0

We get rid of parentheses

x^2-14x-2x+28-45=0

We add all the numbers together, and all the variables

x^2-16x-17=0

a = 1; b = -16; c = -17;
Δ = b2-4ac
Δ = -162-4·1·(-17)
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{-(-16)-18}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+18}{2*1}=\frac{34}{2}
=17
$