2m(m+10)+m=180

Solution for 2m(m+10)+m=180 equation:

2m(m+10)+m=180

We move all terms to the left:

2m(m+10)+m-(180)=0

We add all the numbers together, and all the variables

m+2m(m+10)-180=0

We multiply parentheses

2m^2+m+20m-180=0

We add all the numbers together, and all the variables

2m^2+21m-180=0

a = 2; b = 21; c = -180;
Δ = b2-4ac
Δ = 212-4·2·(-180)
Δ = 1881
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:

$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{209}}{2*2}=\frac{-21-3\sqrt{209}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{209}}{2*2}=\frac{-21+3\sqrt{209}}{4}
$