3+5n=5n(n+2)-7

Solution for 3+5n=5n(n+2)-7 equation:

3+5n=5n(n+2)-7

We move all terms to the left:

3+5n-(5n(n+2)-7)=0


We calculate terms in parentheses: -(5n(n+2)-7), so:

5n(n+2)-7

We multiply parentheses

5n^2+10n-7

Back to the equation:

-(5n^2+10n-7)


We get rid of parentheses

-5n^2+5n-10n+7+3=0

We add all the numbers together, and all the variables

-5n^2-5n+10=0

a = -5; b = -5; c = +10;
Δ = b2-4ac
Δ = -52-4·(-5)·10
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*-5}=\frac{-10}{-10}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*-5}=\frac{20}{-10}
=-2
$