(m-8)(m+6)=3

Solution for (m-8)(m+6)=3 equation:

(m-8)(m+6)=3

We move all terms to the left:

(m-8)(m+6)-(3)=0

We multiply parentheses ..

(+m^2+6m-8m-48)-3=0

We get rid of parentheses

m^2+6m-8m-48-3=0

We add all the numbers together, and all the variables

m^2-2m-51=0

a = 1; b = -2; c = -51;
Δ = b2-4ac
Δ = -22-4·1·(-51)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{13}}{2*1}=\frac{2-4\sqrt{13}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{13}}{2*1}=\frac{2+4\sqrt{13}}{2}
$