7n+n2=54

Solution for 7n+n2=54 equation:

7n+n2=54

We move all terms to the left:

7n+n2-(54)=0

We add all the numbers together, and all the variables

n^2+7n-54=0

a = 1; b = 7; c = -54;
Δ = b2-4ac
Δ = 72-4·1·(-54)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{265}}{2*1}=\frac{-7-\sqrt{265}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{265}}{2*1}=\frac{-7+\sqrt{265}}{2}
$