n^2=35-12n

Solution for n^2=35-12n equation:

n^2=35-12n

We move all terms to the left:

n^2-(35-12n)=0

We add all the numbers together, and all the variables

n^2-(-12n+35)=0

We get rid of parentheses

n^2+12n-35=0

a = 1; b = 12; c = -35;
Δ = b2-4ac
Δ = 122-4·1·(-35)
Δ = 284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{71}}{2*1}=\frac{-12-2\sqrt{71}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{71}}{2*1}=\frac{-12+2\sqrt{71}}{2}
$