x*1.5^2=45000

Solution for x*1.5^2=45000 equation:

x*1.5^2=45000

We move all terms to the left:

x*1.5^2-(45000)=0

Wy multiply elements

x^2-45000=0

a = 1; b = 0; c = -45000;
Δ = b2-4ac
Δ = 02-4·1·(-45000)
Δ = 180000
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:

$\sqrt{\Delta}=\sqrt{180000}=\sqrt{90000*2}=\sqrt{90000}*\sqrt{2}=300\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{2}}{2*1}=\frac{0-300\sqrt{2}}{2}
=-\frac{300\sqrt{2}}{2}
=-150\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{2}}{2*1}=\frac{0+300\sqrt{2}}{2}
=\frac{300\sqrt{2}}{2}
=150\sqrt{2}
$