(m+6)(m-7)=12

Solution for (m+6)(m-7)=12 equation:

(m+6)(m-7)=12

We move all terms to the left:

(m+6)(m-7)-(12)=0

We multiply parentheses ..

(+m^2-7m+6m-42)-12=0

We get rid of parentheses

m^2-7m+6m-42-12=0

We add all the numbers together, and all the variables

m^2-1m-54=0

a = 1; b = -1; c = -54;
Δ = b2-4ac
Δ = -12-4·1·(-54)
Δ = 217
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{217}}{2*1}=\frac{1-\sqrt{217}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{217}}{2*1}=\frac{1+\sqrt{217}}{2}
$