10m(m+1)=m-2

Solution for 10m(m+1)=m-2 equation:

10m(m+1)=m-2

We move all terms to the left:

10m(m+1)-(m-2)=0

We multiply parentheses

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

We get rid of parentheses

10m^2+10m-m+2=0

We add all the numbers together, and all the variables

10m^2+9m+2=0

a = 10; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·10·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*10}=\frac{-10}{20}
=-1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*10}=\frac{-8}{20}
=-2/5
$