-8n+19=-2(8n-3)73n

Solution for -8n+19=-2(8n-3)73n equation:

-8n+19=-2(8n-3)73n

We move all terms to the left:

-8n+19-(-2(8n-3)73n)=0


We calculate terms in parentheses: -(-2(8n-3)73n), so:

-2(8n-3)73n

We multiply parentheses

-1168n^2+438n

Back to the equation:

-(-1168n^2+438n)


We get rid of parentheses

1168n^2-438n-8n+19=0

We add all the numbers together, and all the variables

1168n^2-446n+19=0

a = 1168; b = -446; c = +19;
Δ = b2-4ac
Δ = -4462-4·1168·19
Δ = 110148
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:

$\sqrt{\Delta}=\sqrt{110148}=\sqrt{4*27537}=\sqrt{4}*\sqrt{27537}=2\sqrt{27537}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-446)-2\sqrt{27537}}{2*1168}=\frac{446-2\sqrt{27537}}{2336}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-446)+2\sqrt{27537}}{2*1168}=\frac{446+2\sqrt{27537}}{2336}
$