(6x-5)(9x+6)=0

Solution for (6x-5)(9x+6)=0 equation:

(6x-5)(9x+6)=0

We multiply parentheses ..

(+54x^2+36x-45x-30)=0

We get rid of parentheses

54x^2+36x-45x-30=0

We add all the numbers together, and all the variables

54x^2-9x-30=0

a = 54; b = -9; c = -30;
Δ = b2-4ac
Δ = -92-4·54·(-30)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-81}{2*54}=\frac{-72}{108}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+81}{2*54}=\frac{90}{108}
=5/6
$