1.5x^2=162

Solution for 1.5x^2=162 equation:

1.5x^2=162

We move all terms to the left:

1.5x^2-(162)=0

a = 1.5; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·1.5·(-162)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*1.5}=\frac{0-18\sqrt{3}}{3}
=-\frac{18\sqrt{3}}{3}
=-6\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*1.5}=\frac{0+18\sqrt{3}}{3}
=\frac{18\sqrt{3}}{3}
=6\sqrt{3}
$