3m*6m+4m*m=50

Solution for 3m*6m+4m*m=50 equation:

3m*6m+4m*m=50

We move all terms to the left:

3m*6m+4m*m-(50)=0

Wy multiply elements

18m^2+4m^2-50=0

We add all the numbers together, and all the variables

22m^2-50=0

a = 22; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·22·(-50)
Δ = 4400
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:

$\sqrt{\Delta}=\sqrt{4400}=\sqrt{400*11}=\sqrt{400}*\sqrt{11}=20\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{11}}{2*22}=\frac{0-20\sqrt{11}}{44}
=-\frac{20\sqrt{11}}{44}
=-\frac{5\sqrt{11}}{11}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{11}}{2*22}=\frac{0+20\sqrt{11}}{44}
=\frac{20\sqrt{11}}{44}
=\frac{5\sqrt{11}}{11}
$