x(.75x)=768

Solution for x(.75x)=768 equation:

x(.75x)=768

We move all terms to the left:

x(.75x)-(768)=0

We add all the numbers together, and all the variables

x(+.75x)-768=0

We multiply parentheses

x^2-768=0

a = 1; b = 0; c = -768;
Δ = b2-4ac
Δ = 02-4·1·(-768)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*1}=\frac{0-32\sqrt{3}}{2}
=-\frac{32\sqrt{3}}{2}
=-16\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*1}=\frac{0+32\sqrt{3}}{2}
=\frac{32\sqrt{3}}{2}
=16\sqrt{3}
$