X*(1.5x)=264

Solution for X*(1.5x)=264 equation:

X(1.5X)=264

We move all terms to the left:

X(1.5X)-(264)=0

We add all the numbers together, and all the variables

X(+1.5X)-264=0

We multiply parentheses

X^2-264=0

a = 1; b = 0; c = -264;
Δ = b2-4ac
Δ = 02-4·1·(-264)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{66}}{2*1}=\frac{0-4\sqrt{66}}{2}
=-\frac{4\sqrt{66}}{2}
=-2\sqrt{66}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{66}}{2*1}=\frac{0+4\sqrt{66}}{2}
=\frac{4\sqrt{66}}{2}
=2\sqrt{66}
$