(6q+5)(-9q-8)=0

Solution for (6q+5)(-9q-8)=0 equation:

(6q+5)(-9q-8)=0

We multiply parentheses ..

(-54q^2-48q-45q-40)=0

We get rid of parentheses

-54q^2-48q-45q-40=0

We add all the numbers together, and all the variables

-54q^2-93q-40=0

a = -54; b = -93; c = -40;
Δ = b2-4ac
Δ = -932-4·(-54)·(-40)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-3}{2*-54}=\frac{90}{-108}
=-5/6
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+3}{2*-54}=\frac{96}{-108}
=-8/9
$