(m-3)2-(m-1)(m-5)=0

Solution for (m-3)2-(m-1)(m-5)=0 equation:

(m-3)2-(m-1)(m-5)=0

We multiply parentheses

2m-(m-1)(m-5)-6=0

We multiply parentheses ..

-(+m^2-5m-1m+5)+2m-6=0

We get rid of parentheses

-m^2+5m+1m+2m-5-6=0

We add all the numbers together, and all the variables

-1m^2+8m-11=0

a = -1; b = 8; c = -11;
Δ = b2-4ac
Δ = 82-4·(-1)·(-11)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{5}}{2*-1}=\frac{-8-2\sqrt{5}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{5}}{2*-1}=\frac{-8+2\sqrt{5}}{-2}
$