3e^2=1.5

Solution for 3e^2=1.5 equation:

3e^2=1.5

We move all terms to the left:

3e^2-(1.5)=0

We add all the numbers together, and all the variables

3e^2-1.5=0

a = 3; b = 0; c = -1.5;
Δ = b2-4ac
Δ = 02-4·3·(-1.5)
Δ = 18
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*3}=\frac{0-3\sqrt{2}}{6}
=-\frac{3\sqrt{2}}{6}
=-\frac{\sqrt{2}}{2}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*3}=\frac{0+3\sqrt{2}}{6}
=\frac{3\sqrt{2}}{6}
=\frac{\sqrt{2}}{2}
$