2592=4x(4.5x)

Solution for 2592=4x(4.5x) equation:

2592=4x(4.5x)

We move all terms to the left:

2592-(4x(4.5x))=0

We add all the numbers together, and all the variables

-(4x(+4.5x))+2592=0


We calculate terms in parentheses: -(4x(+4.5x)), so:

4x(+4.5x)

We multiply parentheses

16x^2

Back to the equation:

-(16x^2)


a = -16; b = 0; c = +2592;
Δ = b2-4ac
Δ = 02-4·(-16)·2592
Δ = 165888
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:

$\sqrt{\Delta}=\sqrt{165888}=\sqrt{82944*2}=\sqrt{82944}*\sqrt{2}=288\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-288\sqrt{2}}{2*-16}=\frac{0-288\sqrt{2}}{-32}
=-\frac{288\sqrt{2}}{-32}
=-\frac{9\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+288\sqrt{2}}{2*-16}=\frac{0+288\sqrt{2}}{-32}
=\frac{288\sqrt{2}}{-32}
=\frac{9\sqrt{2}}{-1}
$