3n^2-11n=92

Solution for 3n^2-11n=92 equation:

3n^2-11n=92

We move all terms to the left:

3n^2-11n-(92)=0

a = 3; b = -11; c = -92;
Δ = b2-4ac
Δ = -112-4·3·(-92)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-35}{2*3}=\frac{-24}{6}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+35}{2*3}=\frac{46}{6}
=7+2/3
$