6n^2=35+n

Solution for 6n^2=35+n equation:

6n^2=35+n

We move all terms to the left:

6n^2-(35+n)=0

We add all the numbers together, and all the variables

6n^2-(n+35)=0

We get rid of parentheses

6n^2-n-35=0

We add all the numbers together, and all the variables

6n^2-1n-35=0

a = 6; b = -1; c = -35;
Δ = b2-4ac
Δ = -12-4·6·(-35)
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*6}=\frac{-28}{12}
=-2+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*6}=\frac{30}{12}
=2+1/2
$