180=3m+m(m+10)

Solution for 180=3m+m(m+10) equation:

180=3m+m(m+10)

We move all terms to the left:

180-(3m+m(m+10))=0


We calculate terms in parentheses: -(3m+m(m+10)), so:

3m+m(m+10)

We multiply parentheses

m^2+3m+10m

We add all the numbers together, and all the variables

m^2+13m

Back to the equation:

-(m^2+13m)


We get rid of parentheses

-m^2-13m+180=0

We add all the numbers together, and all the variables

-1m^2-13m+180=0

a = -1; b = -13; c = +180;
Δ = b2-4ac
Δ = -132-4·(-1)·180
Δ = 889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{889}}{2*-1}=\frac{13-\sqrt{889}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{889}}{2*-1}=\frac{13+\sqrt{889}}{-2}
$