(3n+8)(8n-5)=0

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

(3n+8)(8n-5)=0

We multiply parentheses ..

(+24n^2-15n+64n-40)=0

We get rid of parentheses

24n^2-15n+64n-40=0

We add all the numbers together, and all the variables

24n^2+49n-40=0

a = 24; b = 49; c = -40;
Δ = b2-4ac
Δ = 492-4·24·(-40)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-79}{2*24}=\frac{-128}{48}
=-2+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+79}{2*24}=\frac{30}{48}
=5/8
$