1.5n^2=4

Solution for 1.5n^2=4 equation:

1.5n^2=4

We move all terms to the left:

1.5n^2-(4)=0

a = 1.5; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1.5·(-4)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*1.5}=\frac{0-2\sqrt{6}}{3}
=-\frac{2\sqrt{6}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*1.5}=\frac{0+2\sqrt{6}}{3}
=\frac{2\sqrt{6}}{3}
$