(m+5)(m+6)=10

Solution for (m+5)(m+6)=10 equation:

(m+5)(m+6)=10

We move all terms to the left:

(m+5)(m+6)-(10)=0

We multiply parentheses ..

(+m^2+6m+5m+30)-10=0

We get rid of parentheses

m^2+6m+5m+30-10=0

We add all the numbers together, and all the variables

m^2+11m+20=0

a = 1; b = 11; c = +20;
Δ = b2-4ac
Δ = 112-4·1·20
Δ = 41
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{-(11)-\sqrt{41}}{2*1}=\frac{-11-\sqrt{41}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{41}}{2*1}=\frac{-11+\sqrt{41}}{2}
$