10(3n+1)(8n-3)=0

Solution for 10(3n+1)(8n-3)=0 equation:

10(3n+1)(8n-3)=0

We multiply parentheses ..

10(+24n^2-9n+8n-3)=0

We multiply parentheses

240n^2-90n+80n-30=0

We add all the numbers together, and all the variables

240n^2-10n-30=0

a = 240; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·240·(-30)
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-170}{2*240}=\frac{-160}{480}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+170}{2*240}=\frac{180}{480}
=3/8
$