m(m+21)=-108

Solution for m(m+21)=-108 equation:

m(m+21)=-108

We move all terms to the left:

m(m+21)-(-108)=0

We add all the numbers together, and all the variables

m(m+21)+108=0

We multiply parentheses

m^2+21m+108=0

a = 1; b = 21; c = +108;
Δ = b2-4ac
Δ = 212-4·1·108
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3}{2*1}=\frac{-24}{2}
=-12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*1}=\frac{-18}{2}
=-9
$