8n(2n-5)=3(6n-2)

Solution for 8n(2n-5)=3(6n-2) equation:

8n(2n-5)=3(6n-2)

We move all terms to the left:

8n(2n-5)-(3(6n-2))=0

We multiply parentheses

16n^2-40n-(3(6n-2))=0


We calculate terms in parentheses: -(3(6n-2)), so:

3(6n-2)

We multiply parentheses

18n-6

Back to the equation:

-(18n-6)


We get rid of parentheses

16n^2-40n-18n+6=0

We add all the numbers together, and all the variables

16n^2-58n+6=0

a = 16; b = -58; c = +6;
Δ = b2-4ac
Δ = -582-4·16·6
Δ = 2980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2980}=\sqrt{4*745}=\sqrt{4}*\sqrt{745}=2\sqrt{745}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{745}}{2*16}=\frac{58-2\sqrt{745}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{745}}{2*16}=\frac{58+2\sqrt{745}}{32}
$