27=1.5x^2

Solution for 27=1.5x^2 equation:

27=1.5x^2

We move all terms to the left:

27-(1.5x^2)=0

We get rid of parentheses

-1.5x^2+27=0

a = -1.5; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-1.5)·27
Δ = 162
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:

$\sqrt{\Delta}=\sqrt{162}=\sqrt{81*2}=\sqrt{81}*\sqrt{2}=9\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-9\sqrt{2}}{2*-1.5}=\frac{0-9\sqrt{2}}{-3}
=-\frac{9\sqrt{2}}{-3}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+9\sqrt{2}}{2*-1.5}=\frac{0+9\sqrt{2}}{-3}
=\frac{9\sqrt{2}}{-3}
=\frac{3\sqrt{2}}{-1}
$