(x-9)(x-2)=60

Solution for (x-9)(x-2)=60 equation:

(x-9)(x-2)=60

We move all terms to the left:

(x-9)(x-2)-(60)=0

We multiply parentheses ..

(+x^2-2x-9x+18)-60=0

We get rid of parentheses

x^2-2x-9x+18-60=0

We add all the numbers together, and all the variables

x^2-11x-42=0

a = 1; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·1·(-42)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*1}=\frac{28}{2}
=14
$