(m-2)(m-3)=3

Solution for (m-2)(m-3)=3 equation:

(m-2)(m-3)=3

We move all terms to the left:

(m-2)(m-3)-(3)=0

We multiply parentheses ..

(+m^2-3m-2m+6)-3=0

We get rid of parentheses

m^2-3m-2m+6-3=0

We add all the numbers together, and all the variables

m^2-5m+3=0

a = 1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·1·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{13}}{2*1}=\frac{5-\sqrt{13}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*1}=\frac{5+\sqrt{13}}{2}
$