8(x-2)(x-1)=4(x2-4)

Solution for 8(x-2)(x-1)=4(x2-4) equation:

8(x-2)(x-1)=4(x2-4)

We move all terms to the left:

8(x-2)(x-1)-(4(x2-4))=0

We add all the numbers together, and all the variables

-(4(+x^2-4))+8(x-2)(x-1)=0

We multiply parentheses ..

-(4(+x^2-4))+8(+x^2-1x-2x+2)=0


We calculate terms in parentheses: -(4(+x^2-4)), so:

4(+x^2-4)

We multiply parentheses

4x^2-16

Back to the equation:

-(4x^2-16)


We multiply parentheses

8x^2-8x-16x-(4x^2-16)+16=0

We get rid of parentheses

8x^2-4x^2-8x-16x+16+16=0

We add all the numbers together, and all the variables

4x^2-24x+32=0

a = 4; b = -24; c = +32;
Δ = b2-4ac
Δ = -242-4·4·32
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{-(-24)-8}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8}{2*4}=\frac{32}{8}
=4
$