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

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

(X-14)(X-2)=45

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

X^2-2X-14X+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
$