(x+9)(x-6)=2

Solution for (x+9)(x-6)=2 equation:

(x+9)(x-6)=2

We move all terms to the left:

(x+9)(x-6)-(2)=0

We multiply parentheses ..

(+x^2-6x+9x-54)-2=0

We get rid of parentheses

x^2-6x+9x-54-2=0

We add all the numbers together, and all the variables

x^2+3x-56=0

a = 1; b = 3; c = -56;
Δ = b2-4ac
Δ = 32-4·1·(-56)
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{233}}{2*1}=\frac{-3-\sqrt{233}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{233}}{2*1}=\frac{-3+\sqrt{233}}{2}
$