6x(2x-9)=0

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

6x(2x-9)=0

We multiply parentheses

12x^2-54x=0

a = 12; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·12·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*12}=\frac{108}{24}
=4+1/2
$