3n^2+5n=164

Solution for 3n^2+5n=164 equation:

3n^2+5n=164

We move all terms to the left:

3n^2+5n-(164)=0

a = 3; b = 5; c = -164;
Δ = b2-4ac
Δ = 52-4·3·(-164)
Δ = 1993
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{1993}}{2*3}=\frac{-5-\sqrt{1993}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1993}}{2*3}=\frac{-5+\sqrt{1993}}{6}
$