4(5x-4)=4x(5x-5)

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

4(5x-4)=4x(5x-5)

We move all terms to the left:

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

We multiply parentheses

20x-(4x(5x-5))-16=0


We calculate terms in parentheses: -(4x(5x-5)), so:

4x(5x-5)

We multiply parentheses

20x^2-20x

Back to the equation:

-(20x^2-20x)


We get rid of parentheses

-20x^2+20x+20x-16=0

We add all the numbers together, and all the variables

-20x^2+40x-16=0

a = -20; b = 40; c = -16;
Δ = b2-4ac
Δ = 402-4·(-20)·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{5}}{2*-20}=\frac{-40-8\sqrt{5}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{5}}{2*-20}=\frac{-40+8\sqrt{5}}{-40}
$