2m+3m(2)=102

Solution for 2m+3m(2)=102 equation:

2m+3m(2)=102

We move all terms to the left:

2m+3m(2)-(102)=0

We add all the numbers together, and all the variables

3m^2+2m-102=0

a = 3; b = 2; c = -102;
Δ = b2-4ac
Δ = 22-4·3·(-102)
Δ = 1228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1228}=\sqrt{4*307}=\sqrt{4}*\sqrt{307}=2\sqrt{307}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{307}}{2*3}=\frac{-2-2\sqrt{307}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{307}}{2*3}=\frac{-2+2\sqrt{307}}{6}
$