4x(x-2)=3x^2

Solution for 4x(x-2)=3x^2 equation:

4x(x-2)=3x^2

We move all terms to the left:

4x(x-2)-(3x^2)=0

determiningTheFunctionDomain
-3x^2+4x(x-2)=0

We multiply parentheses

-3x^2+4x^2-8x=0

We add all the numbers together, and all the variables

x^2-8x=0

a = 1; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·1·0
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*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*1}=\frac{16}{2}
=8
$