(4x)(3x-8)=x

Solution for (4x)(3x-8)=x equation:

(4x)(3x-8)=x

We move all terms to the left:

(4x)(3x-8)-(x)=0

We add all the numbers together, and all the variables

-1x+4x(3x-8)=0

We multiply parentheses

12x^2-1x-32x=0

We add all the numbers together, and all the variables

12x^2-33x=0

a = 12; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·12·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*12}=\frac{66}{24}
=2+3/4
$