-6+15n=-7(-6+8n)3n

Solution for -6+15n=-7(-6+8n)3n equation:

-6+15n=-7(-6+8n)3n

We move all terms to the left:

-6+15n-(-7(-6+8n)3n)=0

We add all the numbers together, and all the variables

15n-(-7(8n-6)3n)-6=0


We calculate terms in parentheses: -(-7(8n-6)3n), so:

-7(8n-6)3n

We multiply parentheses

-168n^2+126n

Back to the equation:

-(-168n^2+126n)


We get rid of parentheses

168n^2-126n+15n-6=0

We add all the numbers together, and all the variables

168n^2-111n-6=0

a = 168; b = -111; c = -6;
Δ = b2-4ac
Δ = -1112-4·168·(-6)
Δ = 16353
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:

$\sqrt{\Delta}=\sqrt{16353}=\sqrt{9*1817}=\sqrt{9}*\sqrt{1817}=3\sqrt{1817}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-3\sqrt{1817}}{2*168}=\frac{111-3\sqrt{1817}}{336}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+3\sqrt{1817}}{2*168}=\frac{111+3\sqrt{1817}}{336}
$