2n2=105+n

Solution for 2n2=105+n equation:

2n^2=105+n

We move all terms to the left:

2n^2-(105+n)=0

We add all the numbers together, and all the variables

2n^2-(n+105)=0

We get rid of parentheses

2n^2-n-105=0

We add all the numbers together, and all the variables

2n^2-1n-105=0

a = 2; b = -1; c = -105;
Δ = b2-4ac
Δ = -12-4·2·(-105)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-29}{2*2}=\frac{-28}{4}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*2}=\frac{30}{4}
=7+1/2
$