n2+15=n+26

Solution for n2+15=n+26 equation:

n2+15=n+26

We move all terms to the left:

n2+15-(n+26)=0

We add all the numbers together, and all the variables

n^2-(n+26)+15=0

We get rid of parentheses

n^2-n-26+15=0

We add all the numbers together, and all the variables

n^2-1n-11=0

a = 1; b = -1; c = -11;
Δ = b2-4ac
Δ = -12-4·1·(-11)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{5}}{2*1}=\frac{1-3\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{5}}{2*1}=\frac{1+3\sqrt{5}}{2}
$