(X+6)(x-2)-65=0

Solution for (X+6)(x-2)-65=0 equation:

(X+6)(X-2)-65=0

We multiply parentheses ..

(+X^2-2X+6X-12)-65=0

We get rid of parentheses

X^2-2X+6X-12-65=0

We add all the numbers together, and all the variables

X^2+4X-77=0

a = 1; b = 4; c = -77;
Δ = b2-4ac
Δ = 42-4·1·(-77)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-18}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+18}{2*1}=\frac{14}{2}
=7
$