m(10+m)13=138

Solution for m(10+m)13=138 equation:

m(10+m)13=138

We move all terms to the left:

m(10+m)13-(138)=0

We add all the numbers together, and all the variables

m(m+10)13-138=0

We multiply parentheses

13m^2+130m-138=0

a = 13; b = 130; c = -138;
Δ = b2-4ac
Δ = 1302-4·13·(-138)
Δ = 24076
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:

$\sqrt{\Delta}=\sqrt{24076}=\sqrt{4*6019}=\sqrt{4}*\sqrt{6019}=2\sqrt{6019}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-2\sqrt{6019}}{2*13}=\frac{-130-2\sqrt{6019}}{26}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+2\sqrt{6019}}{2*13}=\frac{-130+2\sqrt{6019}}{26}
$