(x-2)(x-3)=13

Solution for (x-2)(x-3)=13 equation:

(x-2)(x-3)=13

We move all terms to the left:

(x-2)(x-3)-(13)=0

We multiply parentheses ..

(+x^2-3x-2x+6)-13=0

We get rid of parentheses

x^2-3x-2x+6-13=0

We add all the numbers together, and all the variables

x^2-5x-7=0

a = 1; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·1·(-7)
Δ = 53
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{53}}{2*1}=\frac{5-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*1}=\frac{5+\sqrt{53}}{2}
$