27n2-19n-8=4-3n-8n2

Solution for 27n2-19n-8=4-3n-8n2 equation:

27n^2-19n-8=4-3n-8n^2

We move all terms to the left:

27n^2-19n-8-(4-3n-8n^2)=0

We get rid of parentheses

27n^2+8n^2+3n-19n-4-8=0

We add all the numbers together, and all the variables

35n^2-16n-12=0

a = 35; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·35·(-12)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-44}{2*35}=\frac{-28}{70}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+44}{2*35}=\frac{60}{70}
=6/7
$