(4x^2-12x+9)-9=81

Solution for (4x^2-12x+9)-9=81 equation:

(4x^2-12x+9)-9=81

We move all terms to the left:

(4x^2-12x+9)-9-(81)=0

We add all the numbers together, and all the variables

(4x^2-12x+9)-90=0

We get rid of parentheses

4x^2-12x+9-90=0

We add all the numbers together, and all the variables

4x^2-12x-81=0

a = 4; b = -12; c = -81;
Δ = b2-4ac
Δ = -122-4·4·(-81)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{10}}{2*4}=\frac{12-12\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{10}}{2*4}=\frac{12+12\sqrt{10}}{8}
$