1.5x2=3

Solution for 1.5x2=3 equation:

1.5x^2=3

We move all terms to the left:

1.5x^2-(3)=0

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

The end solution:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{2}}{2*1.5}=\frac{0-3\sqrt{2}}{3}
=-\frac{3\sqrt{2}}{3}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{2}}{2*1.5}=\frac{0+3\sqrt{2}}{3}
=\frac{3\sqrt{2}}{3}
=\sqrt{2}
$