1.5x^2=9

Solution for 1.5x^2=9 equation:

1.5x^2=9

We move all terms to the left:

1.5x^2-(9)=0

a = 1.5; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·1.5·(-9)
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{6}}{2*1.5}=\frac{0-3\sqrt{6}}{3}
=-\frac{3\sqrt{6}}{3}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{6}}{2*1.5}=\frac{0+3\sqrt{6}}{3}
=\frac{3\sqrt{6}}{3}
=\sqrt{6}
$