(2q-7)(-3q-8)=0

Solution for (2q-7)(-3q-8)=0 equation:

(2q-7)(-3q-8)=0

We multiply parentheses ..

(-6q^2-16q+21q+56)=0

We get rid of parentheses

-6q^2-16q+21q+56=0

We add all the numbers together, and all the variables

-6q^2+5q+56=0

a = -6; b = 5; c = +56;
Δ = b2-4ac
Δ = 52-4·(-6)·56
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-37}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+37}{2*-6}=\frac{32}{-12}
=-2+2/3
$