45=1.5r^2

Solution for 45=1.5r^2 equation:

45=1.5r^2

We move all terms to the left:

45-(1.5r^2)=0

We get rid of parentheses

-1.5r^2+45=0

a = -1.5; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-1.5)·45
Δ = 270
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{270}=\sqrt{9*30}=\sqrt{9}*\sqrt{30}=3\sqrt{30}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{30}}{2*-1.5}=\frac{0-3\sqrt{30}}{-3}
=-\frac{3\sqrt{30}}{-3}
=-\frac{\sqrt{30}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{30}}{2*-1.5}=\frac{0+3\sqrt{30}}{-3}
=\frac{3\sqrt{30}}{-3}
=\frac{\sqrt{30}}{-1}
$