4n^2+8n=77

Solution for 4n^2+8n=77 equation:

4n^2+8n=77

We move all terms to the left:

4n^2+8n-(77)=0

a = 4; b = 8; c = -77;
Δ = b2-4ac
Δ = 82-4·4·(-77)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-36}{2*4}=\frac{-44}{8}
=-5+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+36}{2*4}=\frac{28}{8}
=3+1/2
$