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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6m^2+9m-10m-15)-6=0

We get rid of parentheses

6m^2+9m-10m-15-6=0

We add all the numbers together, and all the variables

6m^2-1m-21=0

a = 6; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·6·(-21)
Δ = 505
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{-(-1)-\sqrt{505}}{2*6}=\frac{1-\sqrt{505}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{505}}{2*6}=\frac{1+\sqrt{505}}{12}
$