9(4x-4)x=5

Solution for 9(4x-4)x=5 equation:

9(4x-4)x=5

We move all terms to the left:

9(4x-4)x-(5)=0

We multiply parentheses

36x^2-36x-5=0

a = 36; b = -36; c = -5;
Δ = b2-4ac
Δ = -362-4·36·(-5)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{14}}{2*36}=\frac{36-12\sqrt{14}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{14}}{2*36}=\frac{36+12\sqrt{14}}{72}
$