3n+8=2n(n+8)

Solution for 3n+8=2n(n+8) equation:

3n+8=2n(n+8)

We move all terms to the left:

3n+8-(2n(n+8))=0


We calculate terms in parentheses: -(2n(n+8)), so:

2n(n+8)

We multiply parentheses

2n^2+16n

Back to the equation:

-(2n^2+16n)


We get rid of parentheses

-2n^2+3n-16n+8=0

We add all the numbers together, and all the variables

-2n^2-13n+8=0

a = -2; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·(-2)·8
Δ = 233
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{-(-13)-\sqrt{233}}{2*-2}=\frac{13-\sqrt{233}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{233}}{2*-2}=\frac{13+\sqrt{233}}{-4}
$