(x-5)(x+9)=9

Solution for (x-5)(x+9)=9 equation:

(x-5)(x+9)=9

We move all terms to the left:

(x-5)(x+9)-(9)=0

We multiply parentheses ..

(+x^2+9x-5x-45)-9=0

We get rid of parentheses

x^2+9x-5x-45-9=0

We add all the numbers together, and all the variables

x^2+4x-54=0

a = 1; b = 4; c = -54;
Δ = b2-4ac
Δ = 42-4·1·(-54)
Δ = 232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{58}}{2*1}=\frac{-4-2\sqrt{58}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{58}}{2*1}=\frac{-4+2\sqrt{58}}{2}
$