3n^2-17n=28

Solution for 3n^2-17n=28 equation:

3n^2-17n=28

We move all terms to the left:

3n^2-17n-(28)=0

a = 3; b = -17; c = -28;
Δ = b2-4ac
Δ = -172-4·3·(-28)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-25}{2*3}=\frac{-8}{6}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*3}=\frac{42}{6}
=7
$