3x*(x-6)-64=0

Solution for 3x*(x-6)-64=0 equation:

3x(x-6)-64=0

We multiply parentheses

3x^2-18x-64=0

a = 3; b = -18; c = -64;
Δ = b2-4ac
Δ = -182-4·3·(-64)
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{273}}{2*3}=\frac{18-2\sqrt{273}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{273}}{2*3}=\frac{18+2\sqrt{273}}{6}
$