(3m+6)(2m+9)=5+(-3)

Solution for (3m+6)(2m+9)=5+(-3) equation:

(3m+6)(2m+9)=5+(-3)

We move all terms to the left:

(3m+6)(2m+9)-(5+(-3))=0

We add all the numbers together, and all the variables

(3m+6)(2m+9)-2=0

We multiply parentheses ..

(+6m^2+27m+12m+54)-2=0

We get rid of parentheses

6m^2+27m+12m+54-2=0

We add all the numbers together, and all the variables

6m^2+39m+52=0

a = 6; b = 39; c = +52;
Δ = b2-4ac
Δ = 392-4·6·52
Δ = 273
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{-(39)-\sqrt{273}}{2*6}=\frac{-39-\sqrt{273}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{273}}{2*6}=\frac{-39+\sqrt{273}}{12}
$