3n2-n=1850

Solution for 3n2-n=1850 equation:

3n^2-n=1850

We move all terms to the left:

3n^2-n-(1850)=0

We add all the numbers together, and all the variables

3n^2-1n-1850=0

a = 3; b = -1; c = -1850;
Δ = b2-4ac
Δ = -12-4·3·(-1850)
Δ = 22201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22201}=149$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-149}{2*3}=\frac{-148}{6}
=-24+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+149}{2*3}=\frac{150}{6}
=25
$