11+m(13-3m)-13m=0

Solution for 11+m(13-3m)-13m=0 equation:

11+m(13-3m)-13m=0

We add all the numbers together, and all the variables

m(-3m+13)-13m+11=0

We add all the numbers together, and all the variables

-13m+m(-3m+13)+11=0

We multiply parentheses

-3m^2-13m+13m+11=0

We add all the numbers together, and all the variables

-3m^2+11=0

a = -3; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-3)·11
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{33}}{2*-3}=\frac{0-2\sqrt{33}}{-6}
=-\frac{2\sqrt{33}}{-6}
=-\frac{\sqrt{33}}{-3}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{33}}{2*-3}=\frac{0+2\sqrt{33}}{-6}
=\frac{2\sqrt{33}}{-6}
=\frac{\sqrt{33}}{-3}
$