m+59=m^2+6m+9

Solution for m+59=m^2+6m+9 equation:

m+59=m^2+6m+9

We move all terms to the left:

m+59-(m^2+6m+9)=0

We get rid of parentheses

-m^2+m-6m-9+59=0

We add all the numbers together, and all the variables

-1m^2-5m+50=0

a = -1; b = -5; c = +50;
Δ = b2-4ac
Δ = -52-4·(-1)·50
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*-1}=\frac{-10}{-2}
=+5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*-1}=\frac{20}{-2}
=-10
$