7(3n+8)(8n-3)=0

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

7(3n+8)(8n-3)=0

We multiply parentheses ..

7(+24n^2-9n+64n-24)=0

We multiply parentheses

168n^2-63n+448n-168=0

We add all the numbers together, and all the variables

168n^2+385n-168=0

a = 168; b = 385; c = -168;
Δ = b2-4ac
Δ = 3852-4·168·(-168)
Δ = 261121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{261121}=511$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(385)-511}{2*168}=\frac{-896}{336}
=-2+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(385)+511}{2*168}=\frac{126}{336}
=3/8
$