562.5=x*1.5x

Solution for 562.5=x*1.5x equation:

562.5=x*1.5x

We move all terms to the left:

562.5-(x*1.5x)=0

We add all the numbers together, and all the variables

-(+x*1.5x)+562.5=0

We get rid of parentheses

-x*1.5x+562.5=0

Wy multiply elements

-1x^2+562.5=0

a = -1; b = 0; c = +562.5;
Δ = b2-4ac
Δ = 02-4·(-1)·562.5
Δ = 2250
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:

$\sqrt{\Delta}=\sqrt{2250}=\sqrt{225*10}=\sqrt{225}*\sqrt{10}=15\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15\sqrt{10}}{2*-1}=\frac{0-15\sqrt{10}}{-2}
=-\frac{15\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15\sqrt{10}}{2*-1}=\frac{0+15\sqrt{10}}{-2}
=\frac{15\sqrt{10}}{-2}
$