(m-8)(m+6)=5

Solution for (m-8)(m+6)=5 equation:

(m-8)(m+6)=5

We move all terms to the left:

(m-8)(m+6)-(5)=0

We multiply parentheses ..

(+m^2+6m-8m-48)-5=0

We get rid of parentheses

m^2+6m-8m-48-5=0

We add all the numbers together, and all the variables

m^2-2m-53=0

a = 1; b = -2; c = -53;
Δ = b2-4ac
Δ = -22-4·1·(-53)
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{6}}{2*1}=\frac{2-6\sqrt{6}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{6}}{2*1}=\frac{2+6\sqrt{6}}{2}
$