(x+8)(x-2)-39=0

Solution for (x+8)(x-2)-39=0 equation:

(x+8)(x-2)-39=0

We multiply parentheses ..

(+x^2-2x+8x-16)-39=0

We get rid of parentheses

x^2-2x+8x-16-39=0

We add all the numbers together, and all the variables

x^2+6x-55=0

a = 1; b = 6; c = -55;
Δ = b2-4ac
Δ = 62-4·1·(-55)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-16}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+16}{2*1}=\frac{10}{2}
=5
$