n2=35+7n

Solution for n2=35+7n equation:

n2=35+7n

We move all terms to the left:

n2-(35+7n)=0

We add all the numbers together, and all the variables

n2-(7n+35)=0

We add all the numbers together, and all the variables

n^2-(7n+35)=0

We get rid of parentheses

n^2-7n-35=0

a = 1; b = -7; c = -35;
Δ = b2-4ac
Δ = -72-4·1·(-35)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{21}}{2*1}=\frac{7-3\sqrt{21}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{21}}{2*1}=\frac{7+3\sqrt{21}}{2}
$