(5q+7)(8q-3)=0

Solution for (5q+7)(8q-3)=0 equation:

(5q+7)(8q-3)=0

We multiply parentheses ..

(+40q^2-15q+56q-21)=0

We get rid of parentheses

40q^2-15q+56q-21=0

We add all the numbers together, and all the variables

40q^2+41q-21=0

a = 40; b = 41; c = -21;
Δ = b2-4ac
Δ = 412-4·40·(-21)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-71}{2*40}=\frac{-112}{80}
=-1+2/5
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+71}{2*40}=\frac{30}{80}
=3/8
$