3m(m+3)=102

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

3m(m+3)=102

We move all terms to the left:

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

We multiply parentheses

3m^2+9m-102=0

a = 3; b = 9; c = -102;
Δ = b2-4ac
Δ = 92-4·3·(-102)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{145}}{2*3}=\frac{-9-3\sqrt{145}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{145}}{2*3}=\frac{-9+3\sqrt{145}}{6}
$