m(2m+1)=105

Solution for m(2m+1)=105 equation:

m(2m+1)=105

We move all terms to the left:

m(2m+1)-(105)=0

We multiply parentheses

2m^2+m-105=0

a = 2; b = 1; c = -105;
Δ = b2-4ac
Δ = 12-4·2·(-105)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*2}=\frac{-30}{4}
=-7+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*2}=\frac{28}{4}
=7
$