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

Solution for 6x+6x-(x^2-9x)-54=0 equation:

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

We add all the numbers together, and all the variables

12x-(x^2-9x)-54=0

We get rid of parentheses

-x^2+12x+9x-54=0

We add all the numbers together, and all the variables

-1x^2+21x-54=0

a = -1; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·(-1)·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-1}=\frac{-6}{-2}
=+3
$