5n=-(n)2+35

Solution for 5n=-(n)2+35 equation:

5n=-(n)2+35

We move all terms to the left:

5n-(-(n)2+35)=0

We add all the numbers together, and all the variables

-(-1n^2+35)+5n=0

We get rid of parentheses

1n^2+5n-35=0

We add all the numbers together, and all the variables

n^2+5n-35=0

a = 1; b = 5; c = -35;
Δ = b2-4ac
Δ = 52-4·1·(-35)
Δ = 165
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{-(5)-\sqrt{165}}{2*1}=\frac{-5-\sqrt{165}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{165}}{2*1}=\frac{-5+\sqrt{165}}{2}
$