9n^2-8+4n=4n

Solution for 9n^2-8+4n=4n equation:

9n^2-8+4n=4n

We move all terms to the left:

9n^2-8+4n-(4n)=0

We add all the numbers together, and all the variables

9n^2-8=0

a = 9; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·9·(-8)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*9}=\frac{0-12\sqrt{2}}{18}
=-\frac{12\sqrt{2}}{18}
=-\frac{2\sqrt{2}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*9}=\frac{0+12\sqrt{2}}{18}
=\frac{12\sqrt{2}}{18}
=\frac{2\sqrt{2}}{3}
$