(X-3)(y-2)=64

Solution for (X-3)(y-2)=64 equation:

(X-3)(X-2)=64

We move all terms to the left:

(X-3)(X-2)-(64)=0

We multiply parentheses ..

(+X^2-2X-3X+6)-64=0

We get rid of parentheses

X^2-2X-3X+6-64=0

We add all the numbers together, and all the variables

X^2-5X-58=0

a = 1; b = -5; c = -58;
Δ = b2-4ac
Δ = -52-4·1·(-58)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{257}}{2*1}=\frac{5-\sqrt{257}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{257}}{2*1}=\frac{5+\sqrt{257}}{2}
$