8x(4x-5)=4x

Solution for 8x(4x-5)=4x equation:

8x(4x-5)=4x

We move all terms to the left:

8x(4x-5)-(4x)=0

We add all the numbers together, and all the variables

-4x+8x(4x-5)=0

We multiply parentheses

32x^2-4x-40x=0

We add all the numbers together, and all the variables

32x^2-44x=0

a = 32; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·32·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*32}=\frac{0}{64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*32}=\frac{88}{64}
=1+3/8
$