n^2+2n/3=4

Solution for n^2+2n/3=4 equation:

n^2+2n/3=4

We move all terms to the left:

n^2+2n/3-(4)=0

We multiply all the terms by the denominator


n^2*3+2n-4*3=0

We add all the numbers together, and all the variables

n^2*3+2n-12=0

Wy multiply elements

3n^2+2n-12=0

a = 3; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·3·(-12)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*3}=\frac{-2-2\sqrt{37}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*3}=\frac{-2+2\sqrt{37}}{6}
$