(6x-3)(9x+4)=0

Solution for (6x-3)(9x+4)=0 equation:

(6x-3)(9x+4)=0

We multiply parentheses ..

(+54x^2+24x-27x-12)=0

We get rid of parentheses

54x^2+24x-27x-12=0

We add all the numbers together, and all the variables

54x^2-3x-12=0

a = 54; b = -3; c = -12;
Δ = b2-4ac
Δ = -32-4·54·(-12)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-51}{2*54}=\frac{-48}{108}
=-4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+51}{2*54}=\frac{54}{108}
=1/2
$