(m^2-m)+(2m+m^2)=69

Solution for (m^2-m)+(2m+m^2)=69 equation:

(m^2-m)+(2m+m^2)=69

We move all terms to the left:

(m^2-m)+(2m+m^2)-(69)=0

We get rid of parentheses

m^2+m^2+2m-m-69=0

We add all the numbers together, and all the variables

2m^2+m-69=0

a = 2; b = 1; c = -69;
Δ = b2-4ac
Δ = 12-4·2·(-69)
Δ = 553
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{-(1)-\sqrt{553}}{2*2}=\frac{-1-\sqrt{553}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{553}}{2*2}=\frac{-1+\sqrt{553}}{4}
$