(m+2)(m+3)=306

Solution for (m+2)(m+3)=306 equation:

(m+2)(m+3)=306

We move all terms to the left:

(m+2)(m+3)-(306)=0

We multiply parentheses ..

(+m^2+3m+2m+6)-306=0

We get rid of parentheses

m^2+3m+2m+6-306=0

We add all the numbers together, and all the variables

m^2+5m-300=0

a = 1; b = 5; c = -300;
Δ = b2-4ac
Δ = 52-4·1·(-300)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*1}=\frac{-40}{2}
=-20
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*1}=\frac{30}{2}
=15
$