x(8-0,5x)=4x^2

Solution for x(8-0,5x)=4x^2 equation:

x(8-0.5x)=4x^2

We move all terms to the left:

x(8-0.5x)-(4x^2)=0

determiningTheFunctionDomain
-4x^2+x(8-0.5x)=0

We add all the numbers together, and all the variables

-4x^2+x(-0.5x+8)=0

We multiply parentheses

-4x^2+0x^2+8x=0

We add all the numbers together, and all the variables

-3x^2+8x=0

a = -3; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-3)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-3}=\frac{0}{-6}
=0
$