3n^2-7n=110

Solution for 3n^2-7n=110 equation:

3n^2-7n=110

We move all terms to the left:

3n^2-7n-(110)=0

a = 3; b = -7; c = -110;
Δ = b2-4ac
Δ = -72-4·3·(-110)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*3}=\frac{-30}{6}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*3}=\frac{44}{6}
=7+1/3
$