2a(-3a)-9(-4)=0

Solution for 2a(-3a)-9(-4)=0 equation:

2a(-3a)-9(-4)=0

We add all the numbers together, and all the variables

2a(-3a)+36=0

We multiply parentheses

-6a^2+36=0

a = -6; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-6)·36
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*-6}=\frac{0-12\sqrt{6}}{-12}
=-\frac{12\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*-6}=\frac{0+12\sqrt{6}}{-12}
=\frac{12\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-1}
$